Washington — President-elect Donald J. Trump spoke by telephone with Taiwan’s president on Friday, a striking break with nearly four decades of diplomatic practice that could precipitate a major rift with China even before Mr. Trump takes office.

Mr. Trump’s office said he spoke with the Taiwanese president, Tsai Ing-wen, “who offered her congratulations.”

He is believed to be the first president or president-elect who has spoken to a Taiwanese leader since 1979, when the United States severed diplomatic ties with Taiwan after its recognition of the People’s Republic of China.

In the statement, Mr. Trump’s office said the two leaders noted that “close economic, political, and security ties” exist between Taiwan and the United States. The statement also said Mr. Trump “congratulated President Tsai on becoming president of Taiwan earlier this year.”

The White House was not told about Mr. Trump’s call until after it happened, according to a senior administration official. The official spoke on ground rules of anonymity to discuss sensitive diplomatic relations.

But the potential fallout from the conversation was significant, the administration official said, noting that the Chinese government issued a bitter protest after the United States sold weapons to Taiwan as part of a well-established arms agreement.

Mr. Trump’s call with President Tsai is a far bigger provocation, though the Chinese government did not issue an immediate response. Beijing views Taiwan as a breakaway province and has adamantly opposed the attempts of any country to open official relations with it.