Senators on the Foreign Relations Committee said they had a deal Tuesday that could lead to a bipartisan vote in favor of giving Congress a vote to approve or disapprove a nuclear deal with Iran.

"We have reached an agreement that absolutely keeps the integrity of the process in place," 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.), the chairman of the panel, said on Bloomberg TV.

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He predicted the legislation would be approved in a bipartisan vote by his panel.

If approved by the House and Senate, the bill would prevent the White House from lifting sanctions on Iran if Congress votes to disapprove of a final agreement.

The White House has threatened to veto Corker's bill, warning it could scuttle talks with Iran on a final nuclear agreement. But Corker has been negotiating with Sen. Ben Cardin Benjamin (Ben) Louis CardinPPP application window closes after coronavirus talks deadlock Congress eyes tighter restrictions on next round of small business help Senate passes extension of application deadline for PPP small-business loans MORE (D-Md.), his panel's ranking member, and Cardin on MSNBC said he thought the deal represented a "fair compromise."

"We've reached an agreement and I'm confident that it will carry out the two major purposes of the bill: an orderly way to review the agreements when they're submitted and the timing... in the event that there's material breaches," he said.

An aide familiar with the deal said the managers’ package will shorten the time Congress has to review a final nuclear deal with Iran from 60 days to 52. President Obama must submit it to Congress by July 9 to enact the expedited schedule.

Under the new timeline, Congress would have 30 days to review an agreement with Iran and pass a resolution of disapproval. The president would have 12 days to act on that resolution. Congress would then have an additional 10 days to respond to an expected veto, the aide explained.

"I think the 30 days allows adequate days for congressional hearings and consideration," Cardin said.

The resolution would be subject to a filibuster in the Senate, meaning it would need 60 votes to be approved. A two-thirds majority in both chambers would be needed to overcome a presidential veto.

The managers’ package will also include a requirement that the administration report regularly on Iran’s support of terrorist organizations and its pursuit of ballistic missile technology and capability, the aide said.

Those reporting requirements will replace a provision that would have required the administration to certify that Iran had renounced support for terrorism. The administration highlighted it as a major concern it had with the bill.

Corker on Monday suggested the agreement he's reached could lead to a strong bipartisan vote.

"I believe we’ve struck an exact right balance in the agreement that will be voted on today and I’m hopeful that we’re going to be very, very successful,” Corker said while appearing on CNN’s “New Day.”

Supporters of the Corker bill have been nearing a majority in the Senate that would be high enough to override a veto. It takes two-thirds majority votes in both chambers to override a veto.

Sen. Chris Murphy Christopher (Chris) Scott MurphyDemocratic senator calls for 'more flexible' medical supply chain to counter pandemics The Hill's 12:30 Report - Presented by Facebook - Don't expect a government check anytime soon GOP chairman to release interim report on Biden probe 'in about a week' MORE (D-Conn.) indicated the changes could turn him into a supporter of the bill.

"I was a hard 'no' on the original bill, so I'm going to talk to the White House about these new changes," he said.

"If the bill stays close to where it is, I'll be as strongly supportive as I have been," said Kaine, an original cosponsor.

Menendez said he expected the committee markup to turn out "very positively."

The first would cut the review period from 60 days to 30 days, while the second would remove a provision requiring that the administration certify as part of a nuclear deal that Iran is no longer supporting terrorist organizations such as Hezbollah.

"By the end of today I am optimistic that we will demonstrate the possibility of a more balanced and bipartisan outcome," Coons said.

Republicans are also expected to offer amendments to the Iran bill, and if they are accepted it could cost the bill support from Democrats.

Corker defended his measure on Tuesday morning from criticism that it constitutes Congress meddling with the executive branch.

“I think there may be a misunderstanding about what’s happening. What Congress is saying is when they finish negotiation — we’re not going to be involved while they’re negotiating — but when they finish we want this presented to Congress,” he said.

--This report was updated at 1:00 p.m.

Jordain Carney and Kristina Wong contributed.