(Reuters) - The U.S. Senate rejected an effort on Wednesday to tie sanctions relief for Iran under an international nuclear agreement to a requirement that President Barack Obamacertify that Tehran is not supporting acts of terrorism against Americans.

A handful of Republicans joined Senate Democrats to reject by a 54-45 vote a proposed amendment offered by Republican Senator John Barrasso that would have added the terrorism clause to a bill subjecting an international nuclear agreement to review by the U.S. Congress.

The Senate has been engaged in intense debate over the legislation, a compromise version of the bill reached in the Senate Foreign Relations Committee last week in an effort to avoid a presidential veto.

Senators Bob Corker and Ben Cardin, the committee's Republican chairman and top Democrat, have been arguing against so-called poison pill amendments seeking to toughen the Iran Nuclear Review Act.

They insist that those amendments would kill its chances of becoming law by alienating Democrats and provoking a veto from Obama, who considers tougher restrictions a threat to ongoing nuclear negotiations between Iran and six world powers.

"We should do everything we can to make sure we have a voice," Corker said in the Senate on Wednesday, as he appealed to lawmakers not to push forward with partisan amendments.

Both of the amendments that have come up so far have been rejected.

The measure voted down on Wednesday sought to reinstate a clause that was removed last week as Democrats and Republicans worked out the compromise version of the bill.