A USA official confirmed the two ships were the USS Mustin and USS Benfold.
Military personnel remain vigilant and are at their stations, the ministry said, adding that it is confident of its capability to maintain regional stability and protect the nation.
"Two U.S. Navy ships conducted a routine transit through the worldwide waters of the Taiwan Strait on July 7-8 (local time)", Captain Charlie Brown, a spokesman for U.S. Pacific Fleet, told Reuters in a statement.
The Tsai administration objects to the consensus because it implies that Taiwan is a part of China, something a majority of Taiwanese do not accept.
Liu said that the people of Taiwan should be able to see through the USA and its intentions and that its behavior has damaged the interests of the people of Taiwan and those of the entire Chinese people, as well as hurting China's interests.
Chinese officials involved in dealing with cross-strait issues should be able to assess the current situation properly, adopt a thoughtful and discreet approach before making comments, and handle cross-strait affairs in a pragmatic manner, the MAC said. The US Navy has not sailed an aircraft carrier in that area since 2007.
The passage of USA military vessels through the Strait and the USS Ronald Reagan previously patrolling the South China Sea are strategic preventive actions adopted by the United States under its Indo-Pacific strategy, an anonymous source familiar with the matter said.
First boys emerge from cave
Monsoon flooding had initially cut off their escape, and rescuers were unable to find them for more than a week. Completing the mission could take up to 3 or 4 days, depending on the weather, rescue operators told Reuters .
China Trade War Starts
The US economy's strength is emboldening the Trump administration to play hardball in its trade offensive against China. He threatened a 10 percent levy on an additional $US200b of Chinese goods if Beijng "refuses to change its practices".
Lewis Hamilton retires from Austrian GP as Max Verstappen wins
When Hamilton did pit, he came back out in fourth place. "We have got the best guys in the pitlane without any shadow of a doubt". On lap 12, Nico Hulkenberg retired, his Renault engine spurting flames. "My gearbox is gone", he told the team.
It has lured away four of Taiwan's diplomatic allies since Tsai came to power, leaving only 18 countries in the world that recognise Taipei over Beijing.
In a move that could heighten tensions between Washington and Beijing, two US Navy destroyers have sailed through the Taiwan Strait, a US Navy official has confirmed to CNN.
U.S. Marines usually guard missions in countries with which Washington has formal diplomatic ties. The U.S. Navy has continued to carry out freedom of navigation passages in worldwide waters close to those islands that have the effect of countering China's territorial claims.
The US also continues to sell advanced weapons to Taiwan to aid in its defense as part of the requirements under the Taiwan Relations Act, actions that are met with condemnation from Beijing.
Beijing has cut off official contacts with Taiwan since Tsai took office because the Tsai administration rejects the "1992 consensus" that provided the foundation for cross-strait relations between China and Taiwan's previous government under the Kuomintang. "So there'll be no rolling back by China".
"If we need to do a comparison, Taiwan certainly ranks above other topical hot-button issues such as even the East and South China sea disputes", Koh said.
Former Taiwan Vice President Lien Chan, of Taiwan's pro-China and former ruling Nationalist Party, is scheduled to meet Chinese President Xi Jinping in Beijing next week.