SINGAPORE — Declaring that “the clock had run out,” Secretary of State Mike Pompeo urged Turkey on Friday to free an American pastor imprisoned on espionage charges, in a case that had spurred United States to impose sanctions against two top Turkish government officials.

Mr. Pompeo discussed the case of the evangelical pastor, Andrew Brunson, with Turkey’s foreign minister, Mevlut Cavusoglu, on the sidelines of a Southeast Asia security conference in Singapore, after previously pressing the case at least three times by phone.

Mr. Brunson’s imprisonment has threatened to plunge fraught relations with Turkey, a vital NATO ally, into crisis.

“The Turks were well on notice that the clock had run out and that it was time for Pastor Brunson to be returned. I hope they’ll see this for what it is: a demonstration that we’re very serious,” Mr. Pompeo told reporters before the meeting, during the short flight from Kuala Lumpur to Singapore.