WASHINGTON—Senate leaders said Thursday that a coronavirus-aid compromise was within reach, but expressed wariness over the underlying political tension and policy disputes.

One day after House Speaker Nancy Pelosi (D., Calif.) and Senate Minority Leader Chuck Schumer (D., N.Y.) signaled they would accept a smaller relief package than they had previously targeted, both parties indicated that shift could help move them closer to reaching an agreement on aid for businesses and families before the year’s end.

“That is at least movement in the right direction,” Senate Majority Leader Mitch McConnell (R., Ky.) said Thursday on the Senate floor. “Compromise is within reach. We know where we agree. We can do this.”

Mrs. Pelosi and Mr. McConnell spoke on Thursday afternoon, according to Mrs. Pelosi’s office. They discussed “their shared commitment to completing” a spending bill and coronavirus-relief package as soon as possible, tweeted Pelosi spokesman Drew Hammill.

On Wednesday, Mrs. Pelosi and Mr. Schumer said renewed negotiations should use a $908 billion bipartisan proposal as their starting point. Democrats had previously coalesced around a $2.4 trillion bill passed earlier in the House.