TEHRAN — Iran’s supreme leader on Wednesday hinted that his country might step up its nuclear program, signaling a possible escalation in an already volatile relationship with Washington after President Trump announced he was pulling the United States out of the 2015 nuclear deal.

Mr. Trump said on Tuesday that the United States would leave the agreement under which Iran agreed to strict limits for 15 years on its development of nuclear fuel. The deal was intended to prevent Iran from developing nuclear weapons, in return for an easing of economic sanctions. But now, Mr. Trump said, the United States will reimpose sanctions.

Iran has always insisted that its uranium enrichment was intended only to operate nuclear power plants and conduct research, but it also put Iran closer to producing fuel that could be used in atomic bombs.

“Last night, you heard the president of America making petty and mindless statements,” Ayatollah Ali Khamenei, Iran’s supreme leader, told a group of teachers in his Tehran office, according to the semiofficial news agency Fars. “There were perhaps more than 10 lies in his statements.”