The shift comes as Mr. Biden has struggled to move much of his agenda through Congress. The Russian invasion of Ukraine, Mr. Biden’s decline in opinion polls, and decades-high inflation have combined to pull many Democrats toward issues they see as better resonating with voters.

“Here’s what this all adds up to: Historic deficit reduction, historic investment in our security at home and abroad by modernizing our capabilities in both areas and an unprecedented commitment to building an economy where everyone has a chance to succeed,” Mr. Biden said of his budget in remarks Monday.

Democrats have narrow control of the House and the 50-50 Senate, and Republicans have lined up against many of the Biden administration’s proposals. Democrats are bracing to lose control of either or both chambers of Congress in the fall’s midterm elections.

The administration is seeking $813 billion for military spending in fiscal year 2023, which begins Oct. 1, a roughly 4% increase from the $782 billion enacted for this fiscal year. Budget figures aren’t adjusted for inflation.

The requested increase is more than double than the 1.6% boost the administration sought for military spending in last year’s budget. The proposal calls for $682 million in funding to go to Ukraine for efforts to counter Russia and shore up its security and economic interests.

The proposed military spending would be the largest ever, if enacted, but it wouldn’t be the biggest one-year increase when compared with some previous years during the wars in Iraq and Afghanistan. The U.S. ended its 20-year war in Afghanistan in August, but is now working to address the crisis in Europe.

U.S. military spending also will likely require additional long-term investments, particularly in the Navy, to stay focused on China as the larger, more strategic threat facing the U.S. Officials say investments in hypersonic missiles, machine learning, artificial intelligence and other military capabilities appropriate for confronting China will require billions of dollars in new investments over time.

While top Democrats cheered the Biden administration’s request, some lawmakers were critical, including Sen. Bernie Sanders (I., Vt.), the chairman of the Senate Budget Committee who caucuses with Democrats.

“At a time when we are already spending more on the military than the next 11 countries combined, no we do not need a massive increase in the defense budget,” Mr. Sanders said.

Senate Minority Leader

Mitch McConnell

(R., Ky.) said the administration’s proposed increase in military funding was inadequate because it doesn’t keep up with the rate of inflation, which rose nearly 8% from a year earlier in February.

“The White House is desperately spinning to call this budget centrist, but there’s nothing remotely moderate about what’s in it,” he said, pointing to the funding increases for nondefense agencies such as the Environmental Protection Agency.

In an interview, Deputy Secretary of Defense

Kathleen Hicks

said the assumptions about inflation might not be accurate in the next several months. “We built this budget on the absolute best inflation information that we had at the time we built it back in the end of ’21,” she said, adding that some provisions were built into the budget that would make it “resilient to inflation.” The budget, she said, also reflects planning since Russia invaded Ukraine the first time, in 2014.

Mr. Biden’s budget also seeks more money for law enforcement. It proposes $17.4 billion for law enforcement at the Justice Department, including $1.7 billion to fight gun trafficking and for other firearm-related efforts, and provides funding for the U.S. Marshals and the Federal Bureau of Investigation to address violent crime. It also calls for funding 300 additional border patrol agent positions.

Overall, the proposal seeks $769 billion for non-defense spending and the medical care program at Veterans Affairs in fiscal 2023, compared with the $691 billion Congress enacted for those items in the current year.

The administration forecasts a yearly drop of roughly 50% in the U.S. deficit during fiscal 2022, to $1.4 trillion, as spending on Covid-19 relief programs wanes and a stronger economy generates more tax revenue.

The budget plans would narrow the deficit by more than $1 trillion relative to where it would stand over a decade under current law. The budget projects debt held by the public would fall to 101.8% of U.S. GDP in fiscal 2023, compared with the White House’s forecast of 102.4% in the current year. Debt is expected to rise in subsequent years to 106.7% of GDP by 2032.

The budget projects “even by their own numbers, that the debt held by the public, which is historically at a high level right now at close to 100%, will continue to grow,” said William Hoagland, senior vice president at the Bipartisan Policy Center and a former senior Republican congressional budget aide.

Mr. Biden and other top Democrats have in recent weeks talked up the party’s work to trim the deficit as they seek to win the support of Sen. Joe Manchin (D., W.Va.) for their stalled economic agenda.

Democrats remain in the early stages of figuring out how to resurrect that agenda—initially called Build Back Better—in a way that can win the support of centrists such Mr. Manchin, who scuttled the House version of the legislation in the Senate. Mr. Manchin has said that he would only support legislation that reduces the deficit, a step that he sees as a way to fight inflation.

Rather than lay out possible ways to overhaul the legislation, the White House budget broadly reiterates the Biden administration’s goals for the bill, listing a series of policy ideas—including free community college—that died during talks among Democrats last year. The tax increases most likely to pass Congress soon, including a surtax on top earners, a 15% minimum tax on corporations and higher taxes on U.S. companies’ foreign earnings, would be part of the revived bill.

Administration officials said they had segmented ideas related to the economic bill away from the broader budget to give space for Democrats on Capitol Hill to continue talking.

Ben Ritz,

director of the Center for Funding America’s Future at the Progressive Policy Institute, said the budget missed an opportunity to provide more direction to Congress about what the bill should look like.

“I can understand why the administration would want to have some distance from the negotiations to let them play out, but the decision to not have detailed policies on Build Back Better creates this big blind spot,” he said “That makes it very difficult to analyze the aggregate fiscal impact of his agenda.”

The budget includes a proposal for a 20% minimum tax rate on income, including unrealized gains in assets, for American households worth more than $100 million. This would apply to the top 0.01% of households, the White House said. That is likely under 20,000 households.

Under current law, capital gains are taxed only when they are realized—when assets are sold—and long-term gains are taxed at lower rates than ordinary income. The White House said that over the next decade the new tax would lower the U.S. deficit by about $360 billion.

The tax, which is unlikely to advance in Congress, could have its biggest impact on billionaires such as

Jeff Bezos

and Mark Zuckerberg, whose fortunes are largely composed of unrealized capital gains in the companies that they founded. Other people might have enough wealth to potentially be subject to the tax but not pay it. That could happen for athletes, entertainers and executives who pay high income-tax rates on their annual earnings.

The Biden administration would also earmark almost $82 billion over five years on preparing for another pandemic and for biodefense, including investing in the making of vaccines.

The budget would start a program to provide uninsured adults access to all recommended vaccines. It also includes $9.9 billion in discretionary funds to build capacity at the Centers for Disease Control and Prevention and at the state and local levels, an increase of $2.8 billion over the 2021 enacted level.

The White House is proposing cutting the nation’s immigration detention capacity by more than 25%, from the 34,000 detention beds Congress funded for this year, down to a proposed 25,000 for next year.

The proposal reflects the administration’s desire to please immigration advocates after a year of maintaining several Trump administration immigration policies, and reflects its goal of releasing more immigrants in the country illegally with ankle bracelets rather than jailing them.

—Richard Rubin, Gordon Lubold, Nancy A. Youssef, Stephanie Armour, Michelle Hackman contributed to this article.

Write to Amara Omeokwe at amara.omeokwe@wsj.com and Andrew Duehren at andrew.duehren@wsj.com