WASHINGTON (Reuters) - U.S. Secretary of State Rex Tillerson faces a tough first trip to Asia this week when the former oil executive will seek to reassure nervous allies facing North Korea’s growing nuclear and missile threat and press China to do more on perhaps the most serious security challenge confronting President Donald Trump.

Tillerson will visit Japan and South Korea before heading to Beijing, where he is expected to firm up a U.S. visit by Chinese President Xi Jinping next month to meet Trump as the leaders of the word’s two largest economies.

But the chances of Tillerson persuading China to do more to curb North Korea’s weapons programs while in Beijing appear scant, given China’s anger at the deployment of a U.S. anti-missile system in South Korea last week, and Trump’s repeated threats to impose punitive tariffs on Beijing to correct a large trade imbalance.

Tillerson faces a delicate task in South Korea, which is in political turmoil after former President Park Geun-hye was ousted last week in a corruption scandal.

The prospects of a victory by South Korea’s liberal opposition in elections to be held within two months, has raised questions about the future there of the U.S.-made Terminal High Altitude Area Defense (THAAD) missile defense system, which China objects to as its radar can penetrate China’s territory.

Beijing has sought to pressure Seoul to drop THAAD.

In Seoul on Friday, Tillerson will meet the acting president, Prime Minister Hwang Kyo-ahn, and Foreign Minister Yun Byung-se. He is not scheduled to see opposition figures, a State Department official said, raising questions about the durability of any agreements.

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China says its influence has limits with neighbor and ally North Korea, which launched four more ballistic missiles last week and is working to develop nuclear-tipped missiles that can reach the United States.

Beijing has proposed that the United States and South Korea halt joint military drills in return for North Korea suspending nuclear and missile activities, an idea Washington and Seoul have rejected.

ROOM FOR MANEUVER WITH CHINA?

A Trump administration official said Tillerson’s position on THAAD would be uncompromising, but suggested there might be room for concessions elsewhere to win more Chinese cooperation on North Korea.

“THAAD is non-negotiable,” the official told Reuters. “This is one of those things where Beijing is just going to have to adapt to or live in a perpetual cycle of outrage.

“But this is a chance to lay down a marker on what we would need from China and to hear from them what they would want to see in return. Everyone is eyes-open that they are not going to give us anything on North Korea without something in return.”

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Tillerson is likely to raise the possibility of “secondary sanctions” on Chinese firms doing business with North Korea.

While the official said “nobody is going to be negotiating core American interests”, there may be other “areas of emphasis” in the U.S.-China relationship to discuss.

“You can only fight on so many fronts at once and given that the North Korean threat is accelerating, there is an opportunity for us to prioritize Chinese assistance there, and perhaps not prioritize areas of disagreement we might otherwise be very vocal about.”

Tillerson will be in China on Saturday and Sunday to meet Xi, State Councilor Yang Jiechi and Foreign Minister Wang Yi.

A media report on Monday said Trump planned to host Xi for a two-day summit tentatively set for April 6-7. The official confirmed the visit was likely next month, including stops by Xi in Washington and Trump’s Mar-a-Lago resort in Florida, but the dates still had to be fixed.

TRIP WILL BE CLOSELY SCRUTINIZED

Tillerson will arrive in Tokyo late on Wednesday for the start of a trip that will be closely watched by those trying to assess how well a former Exxon Mobil executive, who had previously never held public office, can navigate complex and tense diplomatic situations with huge security and economic stakes.

It will also be scrutinized to see to what extent he has Trump’s ear in a White House where factions appear to be competing for influence.

Tillerson, who had dinner with Trump at the White House on Monday, will fly without the normal press contingent on his plane that has traditionally accompanied U.S. secretaries of state since the days of Henry Kissinger in the 1970s.

Tillerson will meet Japanese Prime Minister Shinzo Abe and Foreign Minister Fumio Kishida and are expected to discuss Japan’s plans to step up missile defense and possible deployment of THAAD there, as well as Trump’s concerns about the U.S. trade imbalance with Japan.

The Trump administration is reviewing its policy towards North Korea and has said all options are on the table, including military strikes.

Officials have sought to play down the military option, given the risk of North Korean retaliation. They say sanctions and even an eventual reopening of international talks with North Korea - provided it shows a willingness to halt its weapons programs - are preferred.