A bipartisan group of House lawmakers is pushing to get a vote on the House floor this week for a new authorization for use of military force (AUMF).

The handful of lawmakers sent a letter to the chairman and ranking member of the House Rules Committee, Reps. Pete Sessions Peter Anderson SessionsThe Hill's Campaign Report: New polls show Biden leading by landslide margins The Hill's Morning Report - Presented by Argentum - In Rose Garden, Trump launches anti-Biden screed Pete Sessions wins GOP runoff in comeback bid MORE (R-Texas) and Jim McGovern (D-Mass.), calling for the vote as part of this week’s debate on the annual defense bill.

“As you consider amendments for the House’s debate on this year’s National Defense Authorization Act (NDAA), we urge you to allow debate and a vote on our amendment to replace the two current Authorizations for the Use of Military Force (AUMFs) with an updated one,” the lawmakers wrote in letter dated Monday and released Tuesday.

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The letter was signed by Reps. Mike Coffman Michael (Mike) Howard CoffmanColorado mayor says he called protesters 'domestic terrorists' out of 'frustration' Colorado governor directs officials to reexamine death of Elijah McClain in police custody Petition demanding justice for Elijah McClain surpasses 2 million signatures MORE (R-Colo.), Ruben Gallego Ruben GallegoHispanic caucus report takes stock of accomplishments with eye toward 2021 Senators call on Pentagon to reinstate funding for Stars and Stripes newspaper Hispanic Caucus campaign chief to mount leadership bid MORE (D-Ariz.), Don Bacon (R-Neb.) and Jimmy Panetta James Varni PanettaOn The Money: McConnell previews GOP coronavirus bill | Senate panel advances Trump Fed nominee who recently supported gold standard | Economists warn about scaled-back unemployment benefits Bipartisan bill introduced to provide tax credit to food and beverage distributors Overnight Defense: US formally rejects Beijing's South China Sea claims | House set to consider defense policy bill next week | 57 injured as firefighters battle warship blaze MORE (D-Calif.).

The quartet introduced an amendment to the NDAA that would repeal the 2001 and 2002 AUMFs, replacing them with a measure authorizing military operations against al Qaeda, the Taliban, the Islamic State in Iraq and Syria (ISIS) and associated persons other than a sovereign nation. The authorization would end after five years.

The amendment is identical to a stand-alone resolution the lawmakers introduced last year that has seen no movement in Congress. The group tried to drum up support for their effort in April with a “Dear Colleague” letter. A spokesman for Coffman said the bill gained two co-sponsors after the letter, Reps. Ken Buck Kenneth (Ken) Robert BuckGOP lawmaker says China could use TikTok consumer data against US in a conflict Republicans call for Judiciary hearing into unrest in cities run by Democrats Hillicon Valley: Facebook bans ads from pro-Trump PAC | Uber reports big drop in revenue | US offers M reward for election interference info MORE (R-Colo.) and Jackie Speier Karen (Jackie) Lorraine Jacqueline SpeierOvernight Defense: House to vote on military justice bill spurred by Vanessa Guillén death | Biden courts veterans after Trump's military controversies House to vote on 'I Am Vanessa Guillén' bill Overnight Defense: Trump's battle with Pentagon poses risks in November | Lawmakers launch Fort Hood probe | Military members can't opt out of tax deferral MORE (D-Calif.).

The Trump administration relies on the 2001 AUMF passed in the wake of the Sept. 11, 2001, terrorist attacks for legal authority to prosecute the war against ISIS, as did the Obama administration previously.

In recent years, Congress has had fits and spurts of trying to replace the 2001 AUMF — as well as the 2002 AUMF that authorized the Iraq War — with one more tailored to the ISIS fight. But efforts have consistently stalled amid partisan battles over issues such as when to sunset the authorization.

Most recently, the Senate Foreign Relations Committee has been debating an AUMF introduced by committee Chairman Bob Corker Robert (Bob) Phillips CorkerHas Congress captured Russia policy? Tennessee primary battle turns nasty for Republicans Cheney clashes with Trump MORE (R-Tenn.) and committee member Sen. Tim Kaine Timothy (Tim) Michael KaineButtigieg stands in as Pence for Harris's debate practice Trump meets with potential Supreme Court pick Amy Coney Barrett at White House Names to watch as Trump picks Ginsburg replacement on Supreme Court MORE (D-Va.). But it’s unclear whether that will be more successful as senators appear divided on whether it provides too much power to the executive branch.

In the House, Coffman, Gallego, Bacon and Panetta’s AUMF is one of several attempting to repeal, replace or touch on concerns about the 2001 and 2002 authorizations that have been introduced as amendments to the NDAA.

The House Rules Committee decides which amendments make it to the House floor for a vote and in previous years typically has not advanced AUMFs that were introduced as amendments to the NDAA.

In their letter this week though, the bipartisan group of House lawmakers argued the NDAA is a “particularly appropriate” place to debate a new AUMF.

“Matching defense authorization for critical national security missions with the scope and boundaries provided by a new AUMF just makes sense,” they wrote. “Our bipartisan measure also is important for the men and women in our Armed Forces. A current AUMF lets them know that their continued actions and operations are within the bounds set by the legislative branch of our government.”