The Iranian parliament's national security and foreign affairs committee said it would hold an extraordinary session on Saturday to discuss its response.
"If the enemy steps over part of the agreement, we will do the same, and if they step over the entire deal, we will do the same too," Rouhani said at a cabinet meeting aired by state broadcaster IRIB.
The parliament voted earlier this month to fast-track a bill introduced in June that would increase funds for Iran's missile programme and Revolutionary Guards.
"We must always develop our defence capability and we will strengthen our defensive weapons regardless of the opinion of others," Rouhani said.
The US House passed a new sanctions bill on Tuesday targeting Iran's Revolutionary Guards, as well as Russia and North Korea.
Iran's deputy foreign minister Abbas Araghchi said the bill was "very clearly a hostile measure" even if it was only "a compilation of previous US sanctions in the non-nuclear fields".
Araghchi led the negotiating team that reached the deal with world powers in 2015 known as the JCPOA, under which Iran agreed to strict limits on its nuclear programme in exchange for an easing of sanctions.
The new sanctions bill "can influence the successful implementation of the JCPOA and reduce Iran's benefits under the JCPOA," Araghchi said.
"That's why it is incompatible with various sections of the JCPOA which the US has committed to implement with good intention and in a constructive atmosphere," the ISNA news agency quoted him as saying.
The UN and other signatories to the nuclear deal have agreed that Iran has stuck to its commitments, which has been reluctantly accepted by the administration of President Donald Trump.
"The new US administration has been forced to confirm Iran's loyalty to the deal twice within the past six months and it has had no other option as the IAEA (International Atomic Energy Agency) in various reports has clearly expressed Iran's compliance with its commitments," Araghchi said.
