The United States reimposed harsh sanctions on Iran last November.European allies have stayed in the nuclear deal and have urged Iran to do so, but President Hassan Rouhani of Iran said last month that his country would start leaving parts of it, even though international agencies said Tehran had been abiding by all the terms until now.

Mr. Trump has said in recent weeks that he was open to negotiations with Iran, though he has made no effort to start talks. And he posted on Twitter on Thursday, after the Japanese prime minister, Shinzo Abe, made a visit to Tehran, that he thought it was “too soon to even think about making a deal.”

Mr. Trump has also said he could take military action, while insisting he does not want war. In late May, he announced he was sending an additional 1,500 troops to the Middle East, though that was far less than what some top administration officials had requested.

Mr. Pompeo has made 12 demands of Iran that go far beyond the nuclear issues. In his talks, he has stressed the need to roll back Iran’s “expansionist foreign policy” and tamp down the influence of the political and military groups in Arab nations that are supported by Iran. From his perspective, that includes Hezbollah in Lebanon, the Houthi rebels in Yemen and a constellation of armed groups in Iraq.

“Iran is lashing out because the regime wants our successful ‘maximum pressure’ campaign lifted,” Mr. Pompeo said Thursday. He added that the administration’s policy continues to focus on using diplomatic and economic pressure to “bring Iran back to the negotiating table at the appropriate time.”

While in Switzerland this month, Mr. Pompeo said the administration was ready to talk to Iran with “no preconditions.” But he has not defined the aims of any negotiations. That statement suggested he might be willing to recalibrate the 12 demands he has made of Iran, which Iranian leaders say are unacceptable.

Mr. Trump has said he does not want Iran to have a nuclear weapon. Iran does not have a weapon now and had not made any moves to increase its production rate of nuclear fuel until recent weeks, following the imposition of stringent measures against the country by the United States. Last month, a senior State Department official said the administration’s goal was to ensure Iran does not get within one year of producing enough fuel to make a nuclear weapon — which was the same red line set by the 2015 nuclear deal forged by Mr. Obama and his aides.