Congress in 2010 approved an Iran sanctions bill that was accompanied by a commitment from other U.S. allies to pursue their own sanctions program against Iran. But even then, Sherman and other members warned they would come back with tougher proposals if those sanctions failed to prompt change in Iran.

Among other things, Sherman's bill would sanction companies that enter into long-term petroleum agreements with Iran or buy sovereign debt there. It would also end tax incentives for oil companies in Iran, sanction Iran's Islamic Revolutionary Guard Corps., and prohibit government contracts with companies that do business with Iran.

Sherman's bill has five co-sponsors, including Ed Royce (R-Calif.), who chairs the House Foreign Affairs subcommittee on Terrorism, Nonproliferation and Trade.

Rep. Ileana Ros-Lehtinen (R-Fla.), who chairs the House Foreign Affairs Committee, has indicated she will introduce a bill shortly that would toughen up U.S. sanctions against Syria. Even President Obama is considering sanctions against that country in light of reports of violent protests.

A National Security Council spokesman said on Monday that some response is being weighed in order to "respond to the crackdown and make clear that this behavior is unacceptable."