Washington (CNN) President Donald Trump faces his most critical week of statesmanship so far -- and it will reflect sharp changes of direction he has already wrought in US foreign policy.

Trump will hold his most important meeting with a world leader yet when he welcomes Chinese President Xi Jinping to his Mar-a-Lago resort in Florida on Friday, after putting Beijing on notice that if it does not do more to rein in its ally North Korea over its nuclear program, the US will take tough action.

"China has great influence over North Korea. And China will either decide to help us with North Korea, or they won't," Trump said in an interview with the Financial Times published Sunday. "And if they do that will be very good for China, and if they don't it won't be good for anyone."

Before his crucial first encounter with Xi, Trump will meet Egypt's President Abdel Fattah el-Sisi at the White House on Monday, ending a chill in relations that descended following the Obama administration's pointed criticism of Sisi's human rights record.

Trump will also have talks on Wednesday with another key US Middle Eastern ally, King Abdullah II of Jordan, which are likely to focus on the campaign against ISIS that the Trump administration has escalated across the Jordanian border in Syria and Iraq.

Trump's performance in the trio of meetings will be closely watched — not least because the President's temperament and blunt political style often seem ill-fitted to the well-grooved formalities of international diplomacy. Other world leaders are still trying to get the measure of Trump and are trying to figure out exactly how his "America First" philosophy will reshape the way the United States applies power abroad.

The President's low approval ratings and deepening intrigue over alleged links between his campaign and Russia at a time when Moscow was accused of interfering in the US election have sent his presidency into an early spiral.

Amid the turmoil, Trump has taken some shaky first steps on the global stage.

His most important visitor so far, German Chancellor Angela Merkel, appeared baffled by the President's decision to make a joke about the former US practice of tapping her phone — as he stuck by his baseless allegations that he was wiretapped by former President Barack Obama.

There were also some awkward moments in the Oval Office when Trump failed to shake the German leader's hand before the cameras.

Trump's first foreign visitor was British Prime Minister Theresa May, and the President put her in an awkward political position back home after announcing the first iteration of his travel ban hours after she left the White House.

On the other hand, Trump's meeting with Japanese Prime Minister Shinzo Abe at the White House and round of golf down in Florida went off without a hitch. The Japanese were delighted that Trump reaffirmed US security guarantees to its ally and that Trump's campaign trail demands for Tokyo to pay more of the cost of housing US troops on its soil appeared to be off the table.

A China pivot?

No global relationship is more important than the one between China and the United States. Beijing has never been more powerful in the modern era and Xi is the strongest Chinese leader since Deng Xiaoping, who set his country on the course to capitalism that has helped it emerge as a rising regional superpower more and more ready to challenge US influence in Asia.

US policy towards China is also at a crossroads. Successive US Presidents have sought to bind China into a rules-based system of global trade in a bid to manage its rise and head off a conflict with the incumbent global superpower — the United States. But it is not clear if Trump buys into that formula. His withdrawal from the Trans Pacific Partnership trade deal is seen by many US allies in Asia as handing the diplomatic and economic initiative there to Beijing.

On the campaign trail, Trump accused China of committing "rape" against the United States and "killing" the US economy with its trade policies. After he was elected, he alarmed mainland leaders by accepting a call from Taiwan's President Tsai Ing-wen and suggested he may not sign up to the "One China Policy" that acknowledges the nationalist island as part of China.

Xi reportedly refused to speak to Trump by telephone once he was inaugurated President until he recommitted his administration to the policy — a step he took in a call with the Chinese leader in February, in an early concession to the Chinese side.

The summit at Mar-a-Lago is somewhat of an unknown quantity given Trump's inexperience and unpredictable nature, the lack of a relationship between the two men and uncertainty over the path the White House wants to take with China. The divisive nature of the issues on the table, including trade, Beijing's territorial maneuvers in the South China Sea and Trump's demand for China to do more to rein in North Korea's fast developing missile and nuclear program also mean that it will be tricky to come to common positions.

"The meeting next week with China will be a very difficult one in that we can no longer have massive trade deficits ... and job losses. American companies must be prepared to look at other alternatives," Trump warned in a pair of tweets last week.

But there have also been signs of restraint from the administration going into the meeting. Trump once vowed to brand China a currency manipulator on the first day of his administration but has not done so. There has also been no repeat to Secretary of State Rex Tillerson's apparent warning in his confirmation hearing that China should be denied access to artificial islands it has been building in the South China Sea. In fact, after meeting Xi in Beijing last month, Tillerson used language about the need to avoid confrontation in the relationship that closely mirrored China's own terminology in what some foreign policy observers saw as another diplomatic victory for Beijing.

Warning on North Korea

In the interview with the Financial Times, Trump struck a tough bargaining position, warning, "if China is not going to solve North Korea, we will," in remarks that could hint at a tougher economic sanctions policy that China might oppose or even military action against the Stalinist state.

Successive US Presidents have chafed at China's attitude towards North Korea and called on its leaders to do more to bring unpredictable leader Kim Jong-Un and his late father Kim Jong-Il to heel.

Although China has often expressed irritation with North Korea, it has not so far changed its basic calculation on the issue — namely that it believes the chaos and refugee flows resulting from a collapse of the regime under pressure from the US and its allies would amount to a hugely destabilizing crisis. China also fears that a unified Korea would effectively mean a US-allied neighbor across its border.

Given his rhetoric, Trump is also under pressure to drive a hard bargain with Xi on trade, though at this point it appears the administration is more inclined to target China with enforcement actions rather than slapping tariffs on Chinese goods in a manner that could ignite a trade war that would hurt both nations.

The President is also sending mixed messages, predicting in the Financial Times interview that he could forge a breakthrough with Xi.

"I have great respect for him. I have great respect for China. I would not be at all surprised if we did something that would be very dramatic and good for both countries and I hope so."

Egypt

On Monday, Trump's focus will not be on Asia but on the Middle East. He will engineer a US rapprochement with Sisi, who was heavily criticized by the Obama administration over the coup that overthrew the elected Muslim Brotherhood government and subsequent crackdown on dissent.

Republicans have long seen the Egyptian leader as the kind of strongman in the region who is preferable to the Brotherhood or the kind of chaos that has ripped apart some nations since the Arab Spring uprisings.

Although the Obama administration released aid and military equipment to Egypt that was frozen after the coup, Sisi did not get a trip to the White House under the former President. His invitation so early in the Trump administration is a sign that from now on, the US government will not make Sisi's political behavior an impediment to its relationship with the most populous Arab nation.

And that does not just go for Egypt. White House officials say Trump will take a "private" and "discreet" approach in raising human rights with his foreign counterparts — an issue the administration says is best discussed behind closed doors.

The Trump administration wants to reboot ties to Egypt, according to the officials, primarily through security ties. But economic issues will also be discussed.

The meeting with Abdullah will take place days after the administration appeared to make the fight against ISIS its top priority in Syria, and putting less of an emphasis on the ouster of President Bashar al-Assad, whom the previous administration branded a war criminal and demanded his ouster.