(CNN) Lawmakers in the House are set to vote on Thursday to repeal the 2002 authorization for the use of military force in Iraq and to block funds from being used to wage war with Iran, in an effort to curtail President Donald Trump's military actions in light of heightened tensions with Iran.

Members previously passed both bills in the House's version of the annual National Defense Authorization Act, but the language was stripped from the final version after negotiations with the Republican-held Senate. The effort gained new life after the Trump administration's decision to carry out a strike that killed Iranian General Qasem Soleimani in Iraq in January.

The 2002 Authorization for Use of Military Force, or AUMF, measure, authored by California Democratic Rep. Barbara Lee, calls to repeal the nearly two-decade old authorization used by Presidents George W. Bush and Barack Obama for certain military attacks in Iraq. Members expect a handful of Republicans to side with Democrats on the vote. Earlier in the week, the White House put out a veto threat on the measure -- signaling the administration expected Republicans to vote against it -- before Trump appeared to reverse course by tweeting Wednesday that Republicans should "vote their HEART."

Some officials in the administration have cited the 2002 AUMF as the legal authority used in the strike against Soleimani, including White House national security adviser Robert O'Brien, who said the attack was "fully authorized under the 2002 AUMF." Yet Defense Secretary Mark Esper has instead cited Article II of the Constitution as the authority underpinning the strike.

Lawmakers from both parties have called for more clarity from the White House on its legal justification. House Foreign Affairs Committee Chairman Eliot Engel sent letters to Esper and Secretary of State Mike Pompeo on January 22 demanding an explanation, saying he is "deeply concerned" about the legality of military action in Iraq.

"No existing congressional Authorization for Use of Military Force can legitimately be interpreted as authorizing the strike against Quassem Soleimani or any other Iranian official," the New York Democrat wrote in his letter to Pompeo. "The Administration owes the American people and Congress a clear explanation of how and why it suddenly believes an 18-year-old authorization for the Iraq War can now be used to fight Iran."

After repeatedly pushing him to testify before Congress, Engel announced Tuesday that Pompeo has agreed to appear before the Foreign Affairs Committee for a hearing on the administration's Iran policy. A date for the hearing has not been set yet.

The other measure that will come up in the House on Thursday, introduced by California Democratic Rep. Ro Khanna, would prohibit funds for military offensive attacks against or in Iran without approval from Congress.

"We have to make sure that we're not providing funds for an offensive war," Khanna told CNN in an interview. "I also think that's the central power that Congress has, which is the power of the purse."

Vermont Sen. Bernie Sanders has introduced a companion bill in the Senate.

But Democrats are still a long way from advancing either piece of legislation beyond the House. GOP leaders in the Senate are unlikely to take up the Lee and Khanna measures, and it's not clear that House Democratic leaders are going to fight to ensure they will be included in this year's National Defense Authorization Act.

"We'll get to that when we get to it," House Majority Leader Steny Hoyer told reporters Tuesday when asked if Democrats will draw a red line on the issue in talks with Senate Republicans after the House passes its version of the legislation in the spring.

"Your question is do I believe this is absolutely essential for the NDAA to pass? We didn't believe it was absolutely essential this year," Hoyer said. He added that Democrats "do believe it is absolutely essential, however, to articulate" that going to war "is a decision that the constitutional framers said was the Congress' to make."

Beyond policy disagreements with the Lee and Khanna bills, Republicans have criticized House Democratic leaders for the vehicle they are using to consider the legislation. Instead of bringing Khanna and Lee's measures forward as standalone bills, Democrats have set them up as amendments to an uncontroversial commemorative coins bill that has already passed the Senate.

The procedural maneuver was designed to avoid Republican motions to recommit. Motions to recommit are the last opportunity for the House to debate and amend legislation before final passage.

Republicans, because they are in the minority, often use motions to recommit to hold votes on amendments that advance their priorities or put moderate Democratic members from Trump districts on the spot. Sometimes the amendments are unrelated to the substance of the bills themselves. These votes almost always fall on party lines, but in some cases the amendments have been popular enough to pass, despite Democratic efforts to keep members together.

Khanna told CNN he is "happy with the way leadership structured this," because it allows a clean vote on his legislation.

Democratic leaders have recently designed legislation specifically to avoid motions to recommit -- and thus Republican amendments -- notably using a nonbinding vehicle to advance an Iran War Powers resolution earlier this month. Republicans slammed the move, arguing the nonbinding resolution amounted to a messaging bill. It also drove Rep. Max Rose, a Democratic freshman from New York, to vote against the resolution.

Republicans said the decision to once again maneuver around a potential motion to recommit ices out the minority party during a critical debate on the issue of war.

"I'm offended by the process that you're using to bring this to the floor," Georgia Republican Rep. Rob Woodall said during House debate on the matter Tuesday.