He offered an amendment to cyber legislation calling for the creation of a commission.
His remarks come after a handful of Senate Democrats criticized Republicans on the issue.
The amendment could add another hurdle to the push to pass the cyber bill by the end of the week.
"I can't imagine how he could make this offer with a straight face," Sen. Harry Reid said.
He said there is "no other available alternative" to keep Iran from getting a nuclear weapon.
"It is clear that this is a bad deal," said Majority Leader Kevin McCarthy.
"We're not going to go there," the No. 2 Senate Republican said Tuesday.
"Patient diplomacy can achieve what isolation and hostility cannot," he said.
Cory Bennett 08/04/15 01:41 PM EDT
Sen. Richard Burr (R-N.C.) is sponsoring a cybersecurity information-sharing bill.
The 2016 contender will introduce legislation for public funding of elections.