Zarif has also faced pressure in parliament over his remarks. Dozens of lawmakers asked Rouhani Sunday whether the foreign minister should lose his job over the comments.
Parliament approved the U.S.-educated Zarif in August with 232 votes out of 281. But hard-liners have since made him a lightning rod for criticism of Rouhani's policies.
Zarif, who played a major role in the interim nuclear deal with world powers last month, kept steady despite pressure from hard-liners, who have sharply criticized the agreement. He has tried to assure them that his negotiating team will strongly defend Iran's interest if the U.S. and its allies change course.
The U.S. Congress is weighing new economic sanctions against Iran.
Zarif told state TV Tuesday that any further sanctions on Iran will scuttle the deal.
"I'm sure that Americans know that any new sanctions would be against what they agreed to in the Geneva Plan of Action and it would be a serious breach and would disrupt the deal on their end and they would be responsible," he said.
In Washington, U.S Secretary of State John Kerry urged lawmakers Tuesday to hold off on imposing new punitive measures on Iran, saying forging ahead with new sanctions risks endangering diplomatic efforts to roll back Tehran's nuclear program.
Iran agreed last month to cap its uranium enrichment activities in return for sanctions relief from the West to give Tehran and the world powers six months to try to work out a final deal.
The five permanent members of the U.N. Security Council plus Germany have long sought to curb Iran's nuclear program, fearing that it aim to produce atomic weapons. Iran says its nuclear program is solely for peaceful purposes.
