White House adviser Kellyanne Conway said on Sunday the previous day's attacks "did not help" prospects for a meeting between the two leaders during the United Nations General Assembly this month, but she left open the possibility a meeting could take place.
US Secretary of State Mike Pompeo said last week that Trump may meet Rouhani at the UNGA with "no preconditions".
Trump tweeted about the potential for a Rouhani meeting on Sunday, while attacking the media.
Iran's Ministry of Foreign Affairs on Sunday called the USA allegations "meaningless" and said they were meant to justify actions against Iran. "They should know that this policy has no value for us", said Khamenei, who has the last say on all state matters.
He was referring to a commission within the framework of the Joint Comprehensive Plan of Action, a 2015 agreement that gave Iran the promise of relief from sanctions in return for curbs on its nuclear program.
Friction between the U.S. and Iran have escalated since May a year ago, when Washington unilaterally pulled out of the deal and slapped Tehran with sanctions once again.
Trump explained Monday that sanctions won't be taken off Iran as a requirement for talks, and that's what he meant when he declared "no preconditions". "We're still in the analysis situation", he said, adding that he has encouraged lawmakers to study the classified evidence on the attack in Saudi Arabia.
The administration has undertaken a "maximum pressure" campaign against Iran, which includes withdrawing from the Iran nuclear deal and ratcheting up sanctions.