Washington (AFP) - Secretary of State Mike Pompeo on Saturday urged US governors to resist Chinese pressure to shun Taiwan as he warned that Beijing was increasingly taking its diplomatic battle to the local level.

In an address to state leaders gathered in Washington, Pompeo said that President Donald Trump's administration would step up communication with state and local governments about dealing with China.

"Don't make separate individual deals and agreements with China that undermine our national policy," Pompeo urged.

"I know none of you would do so intentionally. Let us help you make sure we're getting it right."

Pompeo pointed to a threat last year sent to Mississippi's governor that China would cancel investment over his visit to Taiwan.

He also cited a letter by a Chinese diplomat urging state governments not to congratulate Taiwan's President Tsai Ing-wen on her re-election last month and a case in which a high school in Chicago withdrew an invitation to a Taiwanese representative to take part in a climate discussion.

"It's one thing to pressure the secretary of state of the United States of America. It seems quite something else to go after a high school principal," Pompeo said.

"It shows depth. It shows systemization. It shows intent," Pompeo said.

"While these might seem like local matters to some, the cumulative effect is of enormous national importance and international significance," he said.

China considers Taiwan, a self-governing democracy where the mainland's defeated nationalists fled in 1949, to be a territory awaiting reunification.

The United States, like most countries, only recognizes Beijing but the Trump administration has been increasingly vocal in backing Taiwan's right to participate in international bodies and maintain diplomatic relations with other countries.

Pompeo also warned of Chinese pressure on local leaders not to meet Tibet's exiled spiritual leader the Dalai Lama.

And he voiced concern about US state governments' financial choices, saying that Florida's pension fund has invested in a company with ties to surveillance in Xinjiang, the northwestern region where China has detained more than one million Uighur and other Turkic-speaking Muslims.