The United States looks forward to continuity in the Taiwan-U.S. relationship under the new Taiwanese administration and the U.S. commitment to the island is "rock solid", a former senior U.S. official told Taiwan President Tsai Ing-wen on Monday.

Lai Ching-te from Taiwan's ruling Democratic Progressive Party (DPP) won the presidential election on Saturday as expected and will take office on May 20.

In a show of support for the government, a senior administration official said last week that President Joe Biden planned to send an unofficial delegation to the Chinese-claimed island. Taiwan's government rejects Beijing's sovereignty claims.

The Biden administration has feared that the election, transition and new administration would escalate tensions with Beijing, which has pressured Taiwan militarily and economically to assert its sovereignty claims.

Meeting Tsai at the presidential office, former U.S. National Security Advisor Stephen Hadley said he was there to convey from the American people congratulations on the election.

"Taiwan's democracy has set a shining example to the world," Hadley said, in comments released by Tsai's office.

"We are honoured to have the opportunity to meet with you today to reaffirm that the American commitment to Taiwan is rock solid, principled and bipartisan and that the United States stands with its friends," he added.

Hadley said he looked forward to meeting Lai and other political leaders.

"We look forward to continuity in the relationship between Taiwan and the United States under the new administration, and for common efforts to preserve cross-strait peace and stability."

Lai, meeting the group later at party headquarters, said he hoped the United States would continue to support Taiwan and deepen cooperation with the island.

Lai said his administration will "keep defending peace and stability in the Taiwan Strait" as Tsai has done.

China's military has not directly commented on the election, but on Monday its Eastern Theatre Command released footage of naval combat drills in the East China Sea, without giving a detailed location.

"Battle alert, battle alert!" the command said in accompanying text. "The enemy suddenly arrives and the commander quickly issues combat instructions."