By David Brunnstrom

WASHINGTON (Reuters) - China and the United States must avoid being overly suspicious of each other's strategic intentions, China's ambassador to the United States said on Wednesday while looking ahead to the Presidency of Donald Trump.

Trump lambasted China throughout the U.S. election campaign, drumming up headlines with his pledges to slap 45 percent tariffs on imported Chinese goods and to label the country a currency manipulator on his first day in office.

He has also vowed to build up the U.S. Navy in what advisers say will be a strategy to reassure countries in the Asia-Pacific worried about China's assertive pursuit of territorial claims.

China's Washington envoy, Cui Tiankai, told a film screening to commemorate the 1979 normalization of U.S.-China ties that after “a most unusual political season,” it was important to build consensus and identify common ground.

He said both countries were already cooperating on many issues, but added:

"We have to make greater efforts to promote better mutual understanding and we should be careful not to be overly suspicious about each other’s strategic intentions.

"There are people here in the United States who believe that everything that China does is aimed at challenging the United States' s global dominance, and there are people who believe that everything the U.S. is doing is aimed at containing China.

"I think both views are wrong."

There would inevitably be problems and challenges in the next four years, Cui said, "but ... I am quite confident that, on the whole, the relationship will move forward on a stable and right track."

Cui said the countries had a shared responsibility to cooperate on issues such as terrorism and proliferation of weapons of mass destruction.

"We both want stability in the world. We both strive for a stronger global economy, and we both need a better natural environment. Common goals call for a close partnership."

Trump and Chinese President Xi Jinping spoke by phone on Monday and Xi told the U.S. President-elect cooperation was the only choice for the world's two largest economies, while Trump said they had established a "clear sense of mutual respect."

Nevertheless, Trump's election has created uncertainty when Beijing hopes for stability as it faces daunting reform challenges at home, slowing growth and a leadership reshuffle that will assemble a new party elite around Xi in late 2017.

Zbigniew Brzezinski, who as U.S. National Security Adviser drove normalization with China in the late 1970s told the same Washington event the world was watching U.S. political developments "with some stupefaction."

"We are now living in a political system, a worldwide system, that is experiencing a very serious crisis... . (I)t is potentially threatening to both sides, to the well-being of global stability," he said.

"You can have serious political problems in China … there are serious problems in the United States. We don’t know how we will be managing responsibilities in the foreseeable future, given some of the initial warning signals," Brzezinski said.

(This story has been refiled to remove extraneous word from headline)

(Reporting by David Brunnstrom; Editing by Simon Cameron-Moore)