US Senate Foreign Relations Committee Chairman Bob Corker says Iran nuclear deal review bill will come to the Senate floor for a vote as soon as Thursday.
"My sense is that Thursday there's a very good chance that we'll have an overwhelming vote," Corker said.
Republican Senate Majority Leader Mitch McConnell filed a "cloture" motion to end the debate and move to a vote on the bill.
Senators from both parties say they expect strong support for the Iran Nuclear Review Act in the Senate on Thursday.
The bill, agreed as a compromise between the US President Barack Obama administration and senators in the foreign relations committee, would give the Senate the authority to review, approve or reject a possible nuclear agreement between Iran and the US after signed by the president.
The bill provides a 30-day period to the US Congress after the signing of the agreement to review it and decide whether to lift congressional sanctions for the deal to go into effect.
For a rejection of the agreement 60 votes will be required, and in case of a veto 66 senators should vote to override it to nullify a nuclear agreement signed by Obama.
Several Republican senators proposed a total of 67 amendments during the proceedings last week either to make it easier for the Congress to write off the agreement or to add so called “poison pills” that would prompt a veto by Obama.
Senators Marco Rubio (R-Fla.) and Tom Cotton (R-Ark.) proposed an amendment that would require Iran to recognise Israel’s existence before a nuclear agreement, a condition that would kill the agreement.
Iran and six world powers, namely China, France, Russia, the United Kingdom, and the United States, plus Germany, are trying to reach a nuclear agreement before June 30.