Oren Dorell

USA TODAY

Rex Tillerson spent much of his first week as the nation's top diplomat smoothing relations with countries in the wake of President Trump's tweets, phone tirades and threats that roiled allies and adversaries around the world.

The latest example came Thursday night, when Trump told Chinese President Xi Jinping that he would honor the "one-China" policy that has guided U.S.-China relations for 40 years. The two leaders had an "extremely cordial" phone call and invited each other to visit in the future, according to a White House statement.

Trump had caused concern in China after he said on Dec. 11 that his approach to Taiwan, which Beijing considers a breakaway province, would depend on "other things, including trade." Trump later questioned the "one-China" policy, which recognizes the communist leadership in Beijing as China's only legitimate government.

On Wednesday, Trump sent a warm letter from Trump to Xi, a day after Secretary of State Tillerson met with the U.S. president at the White House.

The State Department would not comment on Tillerson’s role in drafting the letter which thanked Xi for his congratulatory letter after Trump's Jan. 20 inauguration, and wished the Chinese people a happy Lantern Festival and prosperous Year of the Rooster.

Tillerson's diplomatic skills confront a world in chaos

The Chinese New Year came Jan. 28 without a mention by the White House, and the two leaders have yet to speak to each other. Trump has managed, however, to offend China by Twitter and other public statements on a range of political, economic and military disputes. They include contacts with Taiwan; charges of unfair trade, and warnings about China's expansion in the South China Sea.

As a result, China’s state-controlled media announced that military officials assessed a greater risk of war with the U.S. under the new American president.

Tillerson, who started his first day at State on Feb. 2, has also smoothed things over with foreign ministers from Mexico and Australia following contentious presidential calls. He also has vowed to maintain good ties with other allies, according to State Department announcements.

Trump's calls and tweets on foreign policy are threatening rivals, allies

Here's a look at some of his diplomatic forays:

Mexico

Tillerson had a “constructive conversation” on Wednesday with Mexican Foreign Minister Luis Videgaray. The two talked about working together on the relationship between both countries, collaborating on law enforcement, migration and security. They also agreed Tillerson would visit Mexico City, though a date wasn’t mentioned.

The tone of the statement was more genial than the impression left after a series of Twitter exchanges and a phone call between Trump and Mexican President Enrique Peña Nieto.

Peña Nieto canceled a planned meeting with Trump over the U.S. president’s insistence that Mexico pay for a border wall that Trump plans to build. Peña Nieto has said Mexico will not pay for the wall.

Australia

Tillerson spoke on Monday to the foreign secretaries of Australia, Japan and South Korea, which State Department’s Acting Spokesman Mark Toner described in a statement as “three of America’s closest allies.”

In each conversation, Tillerson underscored his determination to work closely on regional and global priorities, and “reiterated the administration’s intent to strengthen our military alliances, our economic partnerships, and our diplomatic cooperation,” Toner said.

That conciliatory language is at odds with the combative tone that came across after Trump argued over the weekend with Australian Prime Minister Malcolm Turnbull over an agreement to accept 1,250 refugees rescued at sea by Australia with then-President Obama.

Trump tweeted about the call on Feb. 1, saying "I will study this dumb deal."

The Washington Post, citing unnamed U.S. officials, reported on Feb. 2 that Trump ended the conversation in anger after the Australian leader tried to turn the talk to other issues. The White House denied Trump ended the call.

Israel

On the day he was sworn in, Tillerson spoke with Israeli Prime Minister Benjamin Netanyahu, focusing on “America’s steadfast commitment to its key allies and partners as it works to protect the interests and safety of the American people.”

White House spokesman Sean Spicer also told reporters that day that Israel’s announcement of new settlement construction in the West Bank — on land Palestinians want for a future state — “is not helpful” to establishing a Middle East peace.

Trump’s choice for ambassador to Israel, his personal lawyer, David Friedman, and his chief of international negotiations, Jason Greenblatt, have both said settlements are not an obstacle to peace. And Trump objected on Twitter to the Obama administration's decision to abstain from a United Nations Security Council resolution condemning Israel for settlement activity.