Speaker Paul Ryan Paul Davis RyanKenosha will be a good bellwether in 2020 At indoor rally, Pence says election runs through Wisconsin Juan Williams: Breaking down the debates MORE (R-Wis.) said Tuesday that the House and Senate have struck a deal to pass the upper chamber’s bipartisan bill to roll back strict financial rules enacted by former President Obama.

Ryan told reporters at the Capitol that the House will hold a vote on the Senate bill targeting the Dodd-Frank Act in exchange for the Senate taking up a package of bills from the House Financial Services Committee.

“We've got an agreement on moving different pieces of legislation, so we will be moving the Dodd-Frank bill,” Ryan said.

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Ryan didn’t say when a vote would take place, if it would happen before Memorial Day or what House bills the Senate would take up. House Majority Leader Kevin McCarthy Kevin Owen McCarthyMcCarthy's Democratic challenger to launch first TV ad highlighting Air Force service as single mother Trump asked Chamber of Commerce to reconsider Democratic endorsements: report The Hill's Morning Report - Sponsored by The Air Line Pilots Association - White House moves closer to Pelosi on virus relief bill MORE (R-Calif.), who controls the House floor schedule, said he would announce when the lower chamber will vote on the Senate bill "soon."

The Senate in March passed a bipartisan bill to exempt dozens of banks from the stricter Federal Reserve oversight under Dodd-Frank and scores more from lending restrictions and reporting requirements. The deal, sponsored by Senate Banking Committee Chairman Mike Crapo Michael (Mike) Dean CrapoBottom line Davis: The Hall of Shame for GOP senators who remain silent on Donald Trump Top GOP senator urges agencies to protect renters, banks amid coronavirus aid negotiations MORE (R-Idaho), passed by a 67-31 vote with support from more than a dozen Democrats.

A deal between the House and Senate would clear the way for Congress to pass the biggest changes to the Dodd-Frank financial rules since the law was enacted in 2010. The House and Senate have squabbled over the Senate bill, which Ryan vowed to freeze unless the Senate agreed to take up provisions from the House.

House Financial Services Committee Chairman Jeb Hensarling Thomas (Jeb) Jeb HensarlingLawmakers battle over future of Ex-Im Bank House passes Ex-Im Bank reboot bill opposed by White House, McConnell Has Congress lost the ability or the will to pass a unanimous bipartisan small business bill? MORE (R-Texas) said he was "excited that our negotiations over the last few weeks have culminated in the Senate agreeing to vote on our House bills."

Spokespeople for Crapo and Democratic senators who sponsored the bill declined to comment on Ryan’s remarks.

House Republicans who passed a sweeping rewrite of Dodd-Frank last year initially said the Senate’s bill didn’t go far enough. Hensarling, the architect of that effort, in March said that the Senate bill would stay on Ryan’s desk unless the Senate agreed to consider amending it.

Hensarling had pushed to add to the Senate bill several dozen Financial Services Committee measures meant to boost small business lending and investment. Those bills passed with little to no Democratic opposition.

But he eased off from his pledge to block the bill last month, voicing support for putting the Senate bill on the House floor if the Senate agreed to take up bills from his committee.

There are still several steps congressional leaders must take before the House and Senate could put the deal in action.

House Republicans told The Hill that House and Senate leaders are still working on which House bills the Senate will take up, but were confident that the deal would be finalized.

"The Senate is working in good faith on this and they're trying to find a way for us to be able to get some more of our noncontroversial bills through," Rep. Blaine Luetkemeyer William (Blaine) Blaine LuetkemeyerMissouri Rep. Blaine Luetkemeyer wins GOP primary Five takeaways from Fauci's testimony Yellen, Bernanke urge Congress to extend unemployment benefit boost MORE (R-Mo.), a senior Financial Services panel member, told The Hill. "They are still working on that — trying to work with a couple of senators to see what kind of bills, how many bills they'd be willing to take in a package."

Another Financial Services Committee Republican told The Hill that the House had been given "a firm commitment" from Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellPelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Senate GOP aims to confirm Trump court pick by Oct. 29: report Trump argues full Supreme Court needed to settle potential election disputes MORE (R-Ky.), who's "working to get Democratic support."

McConnell said in a statement that he's been "working closely" with Ryan and Hensarling to get the Senate bill to the Trump’s desk and looks forward to an "additional reform package coming together that can pass the House and Senate this year.”

"I’m glad this will be happening soon," McConnell said.

The tentative deal is welcome news for Republicans eager to scale back Dodd-Frank, and for the bank and credit union groups who've pressured the House to pass the Senate bill.

Senate Democrats who sponsored the deal said further changes could fracture the fragile bipartisan coalition behind their bill. Sen. Mark Warner Mark Robert WarnerIntelligence chief says Congress will get some in-person election security briefings Overnight Defense: Trump hosts Israel, UAE, Bahrain for historic signing l Air Force reveals it secretly built and flew new fighter jet l Coronavirus creates delay in Pentagon research for alternative to 'forever chemicals' House approves bill to secure internet-connected federal devices against cyber threats MORE (D-Va.) said his fellow Democrats agreed to tank the Dodd-Frank legislation if it came back to the Senate with changes.

Senate Republican leadership has also been wary of spending more floor time on the bill with dozens of presidential appointees still waiting for confirmation.

"It's as good as we can do," Rep. Roger Williams John (Roger) Roger WilliamsThe Hill's 12:30 Report - Presented by Facebook - Yoho apologizes for accosting AOC Ocasio-Cortez accosted by GOP lawmaker over remarks: 'That kind of confrontation hasn't ever happened to me' Cook shifts 20 House districts toward Democrats MORE (R-Texas) told The Hill. "I mean, I was originally saying, if you don't blow up the [Consumer Financial Protection Bureau], I'm out of here. But we have to see the big picture, and Main Street and the community banks are just ready for this to happen."

Updated at 3:24 p.m. Melanie Zanona contributed.