(Reuters) - The Republican leader of the U.S. Senate cleared the way on Tuesday for a vote on a bill that would give Congress the power to review an international nuclear agreement with Iran, ending debate over efforts to use the measure to impose more conditions on Tehran.

Republican Senate Majority Leader Mitch McConnell said he had filed a "cloture" motion to begin the process of formally ending debate. Both Democrats and Republicans said they expected the Iran Nuclear Review Act would pass with strong support in the vote scheduled for Thursday.

"If we get to the final vote without additional blowups between now and then, I think it's going to be overwhelmingly supportive," Senator Bob Corker, the chairman of the Foreign Relations Committee, and author of the bill, told reporters at the Capitol.

Corker made a presentation to his fellow Republican senators at a closed-door lunch meeting on Tuesday, urging them to support the measure without major changes.

A dispute among Republican senators over amendments last week had left Senate and foreign relations committee leaders scrambling for a way to move forward with the legislation.

At least 67 amendments to the bill had been offered by Tuesday, all by Republicans, Many were considered "poison pills," which would have killed the bill by alienating too many Democrats for it to pass or, if it did pass, provoking a veto by Democratic President Barack Obama.

One proposed amendment, from Senator Marco Rubio, a Republican presidential candidate, would have required certification that Iran's leaders have publicly accepted Israel's right to exist as a Jewish state.

Opponents said that amendment would have made it impossible for international negotiators to reach a nuclear agreement with Iran. Diplomats from Iran, the United States and five other world powers have set a June 30 deadline for reaching a final pact in which Tehran will curtail its nuclear program in exchange for the removal of crippling economic sanctions.

Negotiators for the European Union and Iran will resume talks on the deal on May 12 in Vienna, joined by officials from six world powers on May 15, the EU said on Tuesday.