After two tense days of waiting, the ruling from Elizabeth MacDonough, the chief parliamentarian, comes as lawmakers make final changes to the bill so that it falls within the Senate’s rules. The reconciliation process places a number of restrictions on what policy measures can be included in the legislation. It also allows Democrats to pass the legislation without GOP support, provided that they lose no votes among their own ranks.

Increasing the minimum wage to $15 an hour by 2025 has been a priority for the party’s progressives, though some moderate Democrats in the Senate had raised concerns about including it in President Biden’s coronavirus relief package. Some had advocated for a smaller increase or voiced concerns about the sharp jump the proposal would mean for tipped wages in restaurants.

State minimum wage levels

“We are deeply disappointed in this decision. We are not going to give up the fight to raise the minimum wage to $15 to help millions of struggling American workers and their families,” Senate Majority Leader Chuck Schumer (D., N.Y.) said Thursday night. “The American people deserve it, and we are committed to making it a reality.”

The sweeping $1.9 trillion aid package would also provide a $1,400 payment to many Americans; extend and enhance federal unemployment assistance; send $350 billion in aid to state and local governments; and pour new funding into vaccine distribution, food stamps and schools.

In order to comply with the Senate’s rules for reconciliation, a measure must be determined to have a meaningful fiscal impact that can’t be “merely incidental” to the policy proposal. Ms. MacDonough ruled the budget impact of the minimum wage increase was “merely incidental” to the policy change.

Republicans applauded the parliamentarian’s decision Thursday night.

“This decision reinforces reconciliation cannot be used as a vehicle to pass major legislative change—by either party—on a simple majority vote,”

Sen. Lindsey Graham

of South Carolina, the top Republican on the Senate Budget Committee, said. “This decision will, over time, reinforce the traditions of the Senate.”

The parliamentarian’s ruling against the wage increase now puts pressure on Democrats to decide if they will abide by the guidance or seek to overturn it. Some progressive Democrats already have pushed to ignore the parliamentarian’s recommendation and approve the measure, an unusual step that the White House and some Senate Democrats have said they would resist.

“I just don’t think we can go back to voters and say ‘Oh, I’m sorry we promised this to you, we couldn’t do it because the parliamentarian ruled we couldn’t do it.’ Voters expect us to fight for this and get it done,”

Rep. Pramila Jayapal

(D., Wash.), chairwoman of the Congressional Progressive Caucus, said earlier Thursday. “It is possible for the chair to decide to include [it] anyway despite the parliamentarian’s ruling.”

Under the chamber’s rules, the presiding officer of the Senate—in this case Vice President

Kamala Harris

—can disregard the parliamentarian’s advice. But such a step would likely give both parties more license to ignore the parliamentarian in future fights. Several Democratic senators have said they would be uncomfortable with rejecting the parliamentarian’s advice in order to raise the minimum wage, as has the White House.

White House press secretary

Jen Psaki

said Mr. Biden was disappointed in the outcome but “respects the parliamentarian’s decision and the Senate’s process.” She said Mr. Biden “will work with leaders in Congress to determine the best path forward, because no one in this country should work full time and live in poverty.”

Some Democrats have explored other ways to try to raise the minimum wage as part of the relief bill that would comply with the chamber’s rules.

Senate Budget Committee Chairman Bernie Sanders (I., Vt.) said Thursday night that he planned to offer an amendment that would seek to remove tax deductions from large companies that don’t pay workers at least $15 an hour and provide incentives to small businesses.

“That amendment must be included in this reconciliation bill,” he said. Senate Finance Committee Chairman

Ron Wyden

(D., Ore.) said in a statement that he was “looking at a tax penalty for mega-corporations that refuse to pay a living wage.”

Republicans have in the past altered reconciliation bills to comply with the parliamentarian’s guidance. When GOP lawmakers tried unsuccessfully to repeal the Affordable Care Act, they ran into problems trying to repeal the individual mandate, the requirement that many individuals buy coverage or pay a penalty. But after conferring with Ms. MacDonough, Republicans altered the bill to leave the mandate in place but set the penalty at zero dollars.

The parliamentarian’s guidance could help Democrats sidestep a different fight over the minimum wage, since at least two centrist Democrats, Sens. Joe Manchin of West Virginia and Kyrsten Sinema of Arizona, opposed including an increase to $15 an hour as part of the reconciliation package.

In the 50-50 Senate, Democrats can’t afford to lose a single vote among their own ranks, with Ms. Harris casting a tie-breaking vote.

Both Mr. Biden and House Speaker

Nancy Pelosi

(D., Calif.) have indicated that they would try to pass stand-alone legislation increasing the minimum wage to $15 an hour if it couldn’t be included in the package that moves through the Senate.

“We will pass a minimum wage bill,” Mrs. Pelosi said Thursday. However, legislation outside of the reconciliation process would need 60 votes in the Senate, where Republicans have criticized the $15 proposal as harmful to businesses.

If Democrats ultimately opt to abide by the parliamentarian’s ruling, they are also likely to face more pressure from the party’s left wing to abandon the filibuster, the 60-vote threshold on most legislation.

The House is expected to narrowly pass the aid bill Friday, which Mrs. Pelosi said Thursday night will include the minimum wage increase. It will then head to the Senate, where it will be changed to comply with the chamber’s rules. The House will then have to approve it again before sending it to the White House.

Republicans have said they support raising the minimum wage but have their own differences about how to do so.

On Thursday, GOP Sens.

Susan Collins

of Maine,

Shelley Moore Capito

of West Virginia and Rob Portman of Ohio joined legislation from GOP Sens.

Mitt Romney

of Utah and Tom Cotton of Arkansas that would raise the minimum wage to $10 an hour over four years, beginning once the pandemic has ended, and require all employers to use E-Verify, which allows them to check prospective workers’ immigration status.

Earlier this week,

Sen. Josh Hawley

(R., Mo.) said he planned to introduce legislation that would award a quarterly tax credit to workers who earn below the median wage of $16.50 an hour, which would be indexed to inflation. The credit would be worth 50% of the difference between the worker’s hourly rate and the median wage for up to 40 hours of work a week.

Earlier this month, the nonpartisan Congressional Budget Office said that raising the minimum wage to $15 by 2025 could deliver raises for 27 million workers and lift 900,000 Americans above the poverty threshold, but it could cost 1.4 million Americans their jobs over the next four years.

The study found the cumulative federal budget deficit from 2021 to 2031 would increase by $54 billion if a $15 federal minimum was enacted, largely because higher prices for goods and services would contribute to an increase in federal spending. That impact is small relative to the last fiscal year’s $3.1 trillion deficit.

—Siobhan Hughes contributed to this article.

Write to Kristina Peterson at kristina.peterson@wsj.com and Andrew Duehren at andrew.duehren@wsj.com