BEIJING — As President Obama made apologetic calls to Asia to cancel his planned trip to the region, China’s leader, Xi Jinping, was taking a star turn in some of the same countries Mr. Obama would have visited.

Mr. Xi this week became the first foreigner to address the Indonesian Parliament, offering billions of dollars in trade to the country that was Mr. Obama’s childhood home. The Chinese leader then moved on to Malaysia, before preparing to attend two Asian summit meetings that Mr. Obama had to abandon because of the government shutdown at home.

With the cancellation of the visits, the much-promoted but already anemic American “pivot” to Asia was further undercut, leaving regional allies increasingly doubtful the United States will be a viable counterbalance to a rising China.

Coming after Mr. Obama’s U-turn on intervention in Syria amid signs of a new American insularity, the revolt in the House of Representatives over health care left many Asians puzzling over America’s messy democracy and wondering if the United States would be able — or willing — to stand up to China in a confrontation.