US Pacific Fleet spokesperson Captain Charlie Brown confirmed two vessels were transiting through the strait but played down the significance of the manoeuvre.
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.
The passage through the Taiwan Strait, the first such one by a U.S. Navy ship in about a year, follows a series of Chinese military drills around the island that have stoked tensions between Taipei and Beijing. The last U.S. Navy aircraft carrier to sail the area was in 2007.
Beijing is perceived as sensitive to USA military vessels traveling through the strait and continues to lay claim to Taiwan, a self-governed, democratic island, which it views as a breakaway province.
Tsai has criticised China for attempting to change the status quo between the two sides and urged the world to "constrain" its ambitions.
Against the backdrop of tense cross-strait relations and U.S. -Sino relations strained by trade issues, the U.S. Navy sailed two of its Arleigh-Burke guided missile destroyers through the strait over the weekend, which it said was a routine voyage that has been carried out for many years.
The move comes as a U.S.
"These days, Taiwan has been under quite a bit of pressure from China- the snatching of multiple countries from Taiwan's already paltry pool of formal diplomatic allies within a short span of time, regular aerial and naval 'island patrols, ' even cyberattacks on the island", Koh said.
Collin Koh, a specialist in regional naval affairs at Singapore's S. Rajaratnam School of International Studies, said the warships' transit was likely a message from the US that it continues to support Taiwan.
"The U.S. sending military ships through the Taiwan Strait is both a demonstration of its continuing support to Taiwan and of its willingness to exercise its maritime rights in China's periphery", said Abraham Denmark, a former deputy assistant secretary of defense for East Asia under President Barack Obama.
Koh also said the move was unlikely to be a one-off, adding that Beijing would continue to apply pressure on Taipei. China regularly says Taiwan is the most sensitive issue in its ties with the United States. "And Taiwan is surely a litmus test for (Chinese President) Xi Jinping's repeated exhortation to protect China's national sovereignty and territorial integrity".