NEW YORK/WASHINGTON, Jan. 12 (Reuters) - A cancellation of all travel by the U.S. State Department this week includes a planned visit to Taiwan by U.S. Ambassador to the United Nations Kelly Craft, a State Department spokeswoman said on Tuesday.

Craft had been due to visit Taiwan from Wednesday to Friday, prompting China to warn that Washington was playing with fire. Secretary of State Mike Pompeo said on Tuesday that all travel this week had been canceled, including his own trip to Europe, as part of the transition to the incoming Biden administration.

But European diplomats and other people familiar with the matter said Luxembourg’s foreign minister and top European Union officials had declined to meet with him during his planned European trip this week.

Craft’s Taiwan trip appeared to be another part of an effort by Pompeo and President Donald Trump’s Republican administration to lock in a tough approach to China before Democratic President-elect Joe Biden takes office on Jan. 20.

Taiwan’s government expressed “understanding and respect” for the decision, but also regret.

“The Ministry of Foreign Affairs regrets that the U.S. Ambassador to the United Nations Kelly Craft cannot lead a delegation to visit Taiwan from Jan. 13 to 15 as scheduled, but welcomes Ambassador Craft to visit at an appropriate time in the future,” it said in a statement.

Craft is due to leave the role when Biden assumes the presidency next week.

China had said it was firmly opposed to the visit. A representative of China’s mission to the United Nations in New York urged Washington to stop “creating obstacles” for the relationship between China and the United States.

“It’s time that the crazy, irrational behaviors of certain people come to a stop,” the Chinese representative said.

Beijing, which claims the self-governed island as its own territory, has been angered by stepped-up support for Taiwan from the Trump administration, including trips to Taipei by top U.S. officials, further straining Sino-U.S. ties. Pompeo on Saturday said he was lifting restrictions on contacts between U.S. officials and their Taiwanese counterparts.

Chinese fighter jets approached the island in August and September during the last two visits - by U.S. Secretary of Health and Human Services Alex Azar and U.S. Under Secretary of State for Economic Growth, Energy, and the Environment Keith Krach, respectively.

While the United States, like most countries, has no formal diplomatic ties with Taiwan, it is the island’s strongest international backer and arms supplier, being obliged to help provide Taiwan with the means to defend itself under the 1979 Taiwan Relations Act.