U.S. House of Representatives Speaker John Boehner on Wednesday called on counterparts in the Senate to act on legislation to fund the Department of Homeland Security, which could face a partial shutdown unless the congressional funding fight is resolved by Friday.

The House is in "wait-and-see mode" until the Senate moves, Boehner told reporters, adding that staff members on both sides of Congress have been talking.

"Until I see what they're going to pass, no decision has been made on the House side," Boehner said.

"It's time for the Senate to do their job," he added.

On Tuesday, U.S. Senate leaders took a tentative step toward resolving the fiscal crisis, which has become part of a Republican showdown over President Barack Obama's executive actions on immigration.

Obama has said he would veto the House-passed measure, which restricts the president's moves aimed at shielding millions of undocumented immigrants from deportation.

Senate Majority Leader Mitch McConnell, in a concession to Democrats in his chamber, said he would hold a vote on a so-called clean funding bill for the department that would not block Obama's actions if Democrats agree to vote on a separate bill halting the presidential immigration order.

Without additional funding, the department faces a partial shutdown on Friday at midnight.