Senators are restarting discussions over a long-stalled bill to formally authorize the war against the Islamic State in Iraq and Syria (ISIS).

Sen. Tim Kaine Timothy (Tim) Michael KaineBiden promises Democratic senators help in battleground states Second GOP senator to quarantine after exposure to coronavirus The Hill's Morning Report - Sponsored by The Air Line Pilots Association - Pence lauds Harris as 'experienced debater'; Trump, Biden diverge over debate prep MORE (D-Va.), a vocal supporter for passing a stand-alone measure, is working with colleagues in both parties to try to "get over the impasse that has stymied" Congress for years.

"Good timing, new administration, working on new ISIS strategy, and there definitely seems to be more interest from the Republican side of the aisle," he told The Hill.

Kaine previously offered an authorization for the use of military force (AUMF) against ISIS with Sen. Jeff Flake Jeffrey (Jeff) Lane FlakeRepublican former Michigan governor says he's voting for Biden Maybe they just don't like cowboys: The president is successful, some just don't like his style Bush endorsing Biden? Don't hold your breath MORE (R-Ariz.) but that bill died in the Foreign Relations Committee amid entrenched policy and political divisions.

Asked if he was using his 2015 bill with Flake as a starting point, Kaine stressed that the legislation is still being hashed out but signaled they are going in a different direction.

"We assumed that we hit an impasse for a reason," he said. "We're looking at it kind of conceptually in a different way. It's not a minor tweak, this way or that way."

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The 2015 bill included a repeal of a 2002 authorization, sunset after three years, and limited the use of U.S. combat ground troops unless U.S. citizens were in danger.

Sen. John McCain John Sidney McCainMcSally says current Senate should vote on Trump nominee Say what you will about the presidential candidates, as long as it isn't 'They're too old' The electoral reality that the media ignores MORE (R-Ariz.), the chairman of the Armed Services Committee, said separately that he is working with Kaine on the ISIS authorization.

Sen. Bob Corker Robert (Bob) Phillips CorkerHas Congress captured Russia policy? Tennessee primary battle turns nasty for Republicans Cheney clashes with Trump MORE (R-Tenn.), who chairs the Foreign Relations Committee, floated that once the Trump administration finalizes its ISIS strategy "that would be a good time to take [an AUMF] back up."

"I agree that when the administration completes their ISIS strategy, when they complete laying out their ISIS plan, that would a very good time for us to have hearings and then look at updating the AUMF," he told The Hill.

He added that he expects the Trump administration will finish its review of its ISIS strategy in the "fairly near future."

Winning Corker's support for a new war authorization would be crucial to it getting through the Senate. The Foreign Relations Committee would need to greenlight the legislation before sending it to the full Senate for a vote.

An ISIS-specific war bill has stalled for years. During the Obama administration, Republicans were wary of taking up an AUMF that would limit the president's authority, while Democrats want to rein in the ability to use ground combat troops.

But the Trump administration, while believing it currently has legal authority, is publicly backing having Congress pass legislation.

Defense Secretary James Mattis backed Congress voting on a war bill during his first public hearing since his confirmation.

"I would take no issue with the Congress stepping forward with an AUMF. I think it'd be a statement of the American people's resolve," Mattis told a Senate Appropriations panel.

Corker has repeatedly said that he believes the Obama administration had the legal authority without Congress passing an additional war bill, and reiterated that he also believes the Trump administration is on sound legal ground.

Trump signed an executive order in late January giving the Pentagon 30 days to hand over a strategy to defeat ISIS.

Corker noted in a Foreign Relations Committee hearing this week that the Pentagon presented a plan to the president but that they are currently "reworking it."

"We do wish for them to come up and lay out their new strategy," he said during the hearing. "I think that will be the appropriate time for us to take up an AUMF."

Rebecca Kheel contributed