Sen. Lindsey Graham (R-S.C.) said Sunday that lawmakers will soon push for another round of sanctions on Iran in an attempt throttle its nuclear program.

Graham told CNN's "State of the Union" that a bipartisan resolution to impose sanctions would come "very soon." Graham acknowledged such a move wouldn't have the force of law, but said "if we back off now, I think that's exactly the wrong signal."

Graham's comments come after Secretary of State John Kerry and foreign ministers from the United Kingdom, France, Russia, China and Germany, the so-called P5+1 group, left Geneva without striking an interim deal with Iran to halt its nuclear effort.

The deal would likely have included some limited sanctions relief, in exchange for Tehran freezing elements of its nuclear program.

France objected to the deal, questioning whether it was harsh enough to prevent Iran from developing weapons capability. Iran insists its nuclear program is for peaceful energy purposes, but western powers fear Tehran is building nuclear bombs.

Graham applauded France's position, saying, "Thank God for France" on the Sunday show.

"You can't trust the Iranians," Graham added.

Graham said the bipartisan resolution he expects from Congress is more an outline of the endgame for negotiations. And while new Iranian President Hassan Rouhani, a moderate, has been more open to talks about his nation's nuclear ambitions, what Graham is angling for would likely be undesirable for Iran.

The resolution, as Graham described it, would require Iran to stop enriching uranium, dismantle its centrifuges, stop a plutonium-producing reactor in Iraq and hand over all highly-enriched uranium to the international community.

"If it ends with anything less, then the world will regret this," Graham said.