Iran secured relief from some Western sanctions in November when it agreed to an interim deal to scale back some of its nuclear enrichment activity.
U.S. Senate Minority Leader Mitch McConnell, R-Ky., said he was wary about Iran's intentions.
"The Iranian regime has carried out its best attempt at a charm offensive to forestall not only the implementation, but the legislative consideration of, even tougher sanctions should the regime fail to fulfill its commitments according to November's interim agreement," he said in a statement Thursday.
Language was inserted into a bill on veterans' affairs in an effort to move the sanctions initiative forward.
American Legion National Cmdr. Daniel Dellinger expressed frustration with the effort, saying veterans' affairs shouldn't be mixed with the Iranian conflict.
"We can deal with Iran, or any other issue unrelated specifically to veterans, with separate legislation," he said in a statement Wednesday.
Senate Majority Leader Harry Reid, D-Nev., said Thursday "now is not the right time to bring a sanctions package to the floor" of the Senate.
The White House said it wouldn't support new sanctions on Iran and would prefer to allow diplomacy to run its course.