TAIPEI, June 22 (Reuters) - A U.S. Coast Guard ship sailed through the Taiwan Strait on Tuesday , the U.S. Navy's 7th Fleet said on Thursday, transiting the sensitive waterway a day after U.S. Secretary of State Antony Blinken completed a rare visit to Beijing.

The strait, which separates China from the democratically governed island of Taiwan, is a frequent source of tension as Beijing steps up its political and military pressure to try to force Taipei to accept Chinese sovereignty.

The U.S. Navy's 7th Fleet said the national security cutter USCGC Stratton conducted a "routine" Taiwan Strait transit on Tuesday "through waters where high-seas freedoms of navigation and overflight apply in accordance with international law".

"Stratton's transit through the Taiwan Strait demonstrates the United States' commitment to a free and open Indo-Pacific. The United States military flies, sails and operates anywhere international law allows," the 7th Fleet added in its statement.

The mission, which neither China nor Taiwan has yet commented on, happened the day after Blinken ended a visit to Beijing, in which the two countries agreed to stabilise their intense rivalry so it does not veer into conflict, but failed to produce any major breakthrough.

U.S. military vessels, and on occasion those of its allies, have routinely sailed through the strait in recent years, to the anger of China, which views such missions as provocation.

This month the U.S. Navy released a video of an "unsafe interaction" in the strait, in which a Chinese warship crossed in front of a U.S. destroyer operating with a Canadian warship.

Taiwan's military reports almost daily Chinese incursions in the strait, mostly warplanes that cross the waterway's median line, which once served as an unofficial barrier between the two.

On Wednesday, Taiwan said Chinese warships led by the aircraft carrier Shandong sailed through the strait.