Facing new political hurdles at home, President Obama sought to project U.S. strength abroad as he began a week-long trip to the Asia-Pacific region on Monday, touting a growing economy and American leadership at a gathering of nations that are also being wooed by China.

Obama’s pitch at the Asia-

Pacific Economic Cooperation (APEC) summit here came less than a week after Republicans won control of the Senate for the first time in seven years. But the president did not mention that setback during public remarks on the first day of a three-day visit to Beijing.

Instead, Obama pushed forward on efforts to establish deeper economic partnerships in a region that his administration has pledged to make a cornerstone of its foreign policy. He met with leaders of 11 nations that are negotiating a sweeping free-trade pact with the United States, an effort that could be among the few areas of symbiosis with congressional Republicans.

And Obama announced a deal between the United States and China that eases short-term visa restrictions for students, tourists and businesses — a move that he said was aimed at increasing tourism and promoting closer ties between the world’s two largest economies.

Citing U.S. efforts to combat Ebola in West Africa and the Islamic State militant group in Iraq and Syria, Obama told an audience of business executives: “The one constant is and has been American leadership. That has been backed by renewed strength of the economy at home. The American economy . . . is more primed to lead in the 21st century than any other nation on Earth.”

1 of 17 Full Screen Autoplay Close Skip Ad × APEC’s shirt tradition View Photos It’s customary for world leaders to don traditional shirts for a group “family” photo at the Asia-Pacific Economic Cooperation summit. President Obama tried to do away with the “silly shirts,” but this year, they’re back. Caption It’s customary for world leaders to don traditional shirts for a group photo. Nov. 10, 2014 President Obama and Chinese President Xi Jinping walk together at the Water Cube, or National Aquatic Center, before a welcome banquet for the Asia-Pacific Economic Cooperation summit in Beijing. Sergei Ilnitsky/European Pressphoto Agency Buy Photo Wait 1 second to continue.

The president’s arrival at the summit comes at a time when Chinese state-run media have characterized him as diminished and weakened in the wake of the GOP’s rout of Democrats in the midterm elections.

Chinese President Xi Jinping has spent the run-up to the APEC summit presenting a rising China as an alternative to U.S. leadership in Asia, and Russian President Vladi­mir Putin’s presence here this week highlights another challenge to the Obama administration in a region where American allies have raised concerns about the staying power of the United States. Obama and Putin interacted only briefly after a group photo session of all 21 APEC leaders, but White House aides said the two leaders did not discuss anything of substance.

Obama sought to counter the regional fears that the United States was falling behind, as he held bilateral meetings with Australian Prime Minister Tony Abbott and new Indonesian President Joko Widodo.

“There should be no doubt that the United States of America remains entirely committed when it comes to Asia,” Obama said. “The United States is not just here in Asia to check a box. We believe our shared future is here in Asia.”

His remarks came as he prepared for series of formal meetings with Xi starting Tuesday, and Obama carefully calibrated his tone when it came to his Chinese counterpart. He chided Beijing as failing to respect intellectual property rights and condoning cyberspying on U.S. companies. In the latest case, China is suspected of breaching U.S. Postal Service computers. But Obama emphasized that “the United States welcomes the rise of a prosperous, peaceful and stable China.”

The president offered only the mildest criticism of Beijing’s handling of the large pro-democracy demonstrations in Hong Kong over the past several months.

“We don’t expect China to follow the American model in every instance, but we continue to have concerns over human rights,” Obama said. “Obviously, the situation between China and Hong Kong historically has been complicated and is in the process of transition. Our primary message has been to make sure violence is avoided as the people of Hong Kong sort through the next phase of what their relationship is to the mainland.”

President Obama attends a meeting with leaders from the Trans-Pacific Partnership at the U.S. Embassy in Beijing on Monday. (Mandel Ngan/Agence France-Presse via Getty Images)

Obama also spoke for the first time about the release over the weekend of two U.S. citizens who had been held in North Korea — a deal brokered in secret by Director of National Intelligence James R. Clapper Jr. The president said Clapper did not talk with North Korean officials about broader U.S. concerns about Pyongyang’s nuclear program.

“They were not high-level policy discussions,” he said. “But we have been consistent in saying when and if North Korea becomes serious about the denuclearization of the peninsula, we’re prepared to have a conversation.”

Obama’s trip to China, Burma and Australia, planned more than a year ago, has allowed him to turn away — however briefly — from the pending power shift on Capitol Hill. Three years ago, his administration declared that it would “pivot” U.S. military, economic and diplomatic resources to the Asia-Pacific region, as the U.S. wars in Iraq and Afghanistan wound down.

The progress toward that goal has been slow, however, and Obama’s decision to authorize a military campaign against the Islamic State has diverted attention and resources from Asia.

The president hopes to rejuvenate his Asia strategy this week by breathing new life into the 12-member Trans-Pacific Partnership (TPP) free-trade pact, which has been bogged down in disputes over agriculture and intellectual property.

Meeting with leaders of the 11 other nations, Obama said: “It’s up to all of us to see if we can finalize a deal that’s both ambitious and comprehensive. This has the potential to be a historic agreement.”

Administration officials believe the trade pact could spur U.S. investment in the region at a time when the United States is facing increasing economic competition from China along the Asia-Pacific rim stretching from Japan to Australia, two nations that are involved in the negotiations. China is not involved in the TPP talks and has viewed the effort skeptically.

U.S. negotiators said they hope to have an agreement in the first half of next year, which could give Congress enough time to approve a final deal before U.S. political attention turns toward the 2016 presidential race.

In a news conference last week, Senate Minority Leader Mitch McConnell (R-Ky.), who stands to become majority leader in January, said trade was one area in which he believes Republicans can work with the president.

The question is how forcefully Obama will push Congress for the fast-track authority that Democrats denied him this year in the run-up to the elections. The administration said it wants the authority — granting the president the power to finalize a deal that could not be amended by the legislative branch — so that the other countries can be confident in the terms the United States puts on the table in the final stages of negotiations. Japan and the United States have the largest number of remaining disagreements.

“Opposition to the sort of deal that has been written to date is growing,” said Lori Wallach, director of Global Trade Watch, a division of Public Citizen, which is against the pact.

On the visa deal with China, the administration said the new rules would lengthen the validity of short-term tourist and business visas issued to each other’s citizens from one to 10 years — the longest period possible under U.S. law — and increase the validity of student and exchange visas from one to five years.