"If America wants to go back to the experience (of imposing sanctions), Iran would certainly return in a short time - not a week or a month but within hours - to conditions more advanced than before the start of negotiations," Rouhani told a session of parliament broadcast live on state television.
Iran says new U.S. sanctions breach the agreement it reached in 2015 with the United States, Russia, China and three European powers in which it agreed to curb its nuclear work in return for the lifting of most sanctions.
U.S. Ambassador to the United Nations Nikki Haley said the new U.S. sanctions were unrelated to the Iran nuclear deal and that Iran must be held responsible for "its missile launches, support for terrorism, disregard for human rights, and violations of U.N. Security Council resolutions."
"Iran cannot be allowed to use the nuclear deal to hold the world hostage ... The nuclear deal must not become 'too big to fail'," Haley said in a statement on Tuesday, responding to Rouhani.
Haley will travel to Vienna next week to discuss Iran's nuclear activities with U.N. atomic watchdog officials as part of Washington's review of Tehran's compliance with the 2015 nuclear deal.
U.N. Secretary-General Antonio Guterres "considers the (Iran nuclear deal) to be one of the utmost diplomatic achievements in our collective search for peace and security," U.N. spokesman Stephane Dujarric told reporters.
"We need to do whatever we can to preserve it," Dujarric said.