Tillerson earlier said changes were needed in the nuclear deal before the would agree to continue supporting it.
The president argued that Iran is violating the "spirit" of the deal and therefore directed aides to seek tougher enforcement of its nuclear activities and possibly impose new sanctions for its destabilising behaviour in the region.
Under the USA law, Trump has time till October 15 to certify that Iran is complying with the nuclear deal.
Trump on Thursday criticised Iran's behaviour with regard to the 2015 pact.
The president has been weighing whether the agreement serves United States security interests as he faces an October 15 deadline for certifying that Iran is complying with its terms.
If Trump were to decertify the agreement, the decision would be left to Congress as to whether economic sanctions would be returned to Iran. "The President's team has presented a united strategy that the national security team all stands behind and supports,"she said". In exchange, the USA and its allies would lift numerous sanctions that have wrecked the Iranian economy. Previously, Trump had said Iran hasn't lived up to the "spirit" of the worldwide agreement.
"Iran? ISIS? What storm, Mr. President?" a reporter asked.
As part of the landmark 2015 deal, Tehran agreed to curtail its nuclear activities in exchange for relief from global sanctions.
"We have the world's great military people in this room, I will tell you that", Trump said.
At a photo opportunity with the officials following the meeting, Trump addressed the reporters present, saying, "You guys know what this represents?"
Last month, the top US military officer said Iran was complying with the pact curbing its nuclear program and warned that any American decision to walk away from it would make other nations less likely to enter into agreements with the United States.