WASHINGTON, May 17 (Reuters) -

The United States is "sitting by the phone" but has heard no message yet from Iran that it is willing to accept President Donald Trump's overtures for direct talks, a senior Trump administration official said on Friday.

"We think they should de-escalate and come to negotiations," the official, who declined to be identified, told a small group of reporters.

Trump has urged Iran's leadership to hold talks over its nuclear program and regional influence amid rising tensions between the two countries that has fanned fears of armed conflict after the United States deployed an aircraft carrier group to the region.

Asked if there were any indications from the Iranians that they were ready to engage, the official said: "Not yet. We're sitting by the phone."

Trump has communicated to his national security team and other aides that he wants to keep tensions with Tehran from boiling over into a war, but he has also made clear that he will protect U.S. interests in the region, U.S. officials said.

U.S. intelligence showed heightened activity by Iran or its proxies that U.S. officials took as a threat against American targets in the region.