Each of the four countries on Obama's itinerary - Japan, South Korea, Malaysia and the Philippines - has a dispute with Beijing over islands in the South and East China Seas. Their leaders will be weighing Obama's willingness to support them if those conflicts boil over.
''What we can say after seeing what happened to Ukraine is that using force to change the status quo is not acceptable,'' said Japanese Prime Minister Shinzo Abe, whose country is in one of the fiercest disputes with China.
Administration officials, including Defense Secretary Chuck Hagel, have taken a tougher line on the territorial issues in recent weeks, sternly warning China against the use of military force and noting that the U.S. has treaty obligations to defend Japan in particular. But in an attempt to maintain good relations with China, the U.S. has not formally taken sides on the question of which countries should control which islands.
Analysts say there are concerns that China could be emboldened by the relative ease with which Russia annexed the Crimean Peninsula from Ukraine over U.S. objections, as well as the very real possibility that Moscow could take more land. Moreover, some in Asia question Obama's ability to follow through on his security pledges in light of his decision last summer to pull back on plans for a military strike against Syria.
''The heavyweights in the region got very scared by the Syrian decision,'' said Douglas Paal, a longtime U.S. diplomat in Asia who now is vice president of the Carnegie Endowment for International Peace. ''They've never seen anything like that. They've always counted on strong executives bringing the Congress along or going around the Congress to make sure that our security guarantees will be honored.''
Obama's advisers say they see little evidence thus far that China has been encouraged by Russia's incursions into Ukraine. Instead, they say Beijing appears to be viewing with concern the Kremlin's attempts to sway pro-Russian populations in areas of Ukraine, given China's own restive minority populations in border regions.
U.S. officials also have tried to keep China from supporting Russia's moves in Ukraine by appealing to Beijing's well-known and vehement opposition to outside intervention in other nations' domestic affairs. Officials say they plan to emphasize that stance when they discuss Asia's territorial disputes with regional leaders this week.
''We have been talking with them about the importance of a strong international front to uphold principles that they and we all hold dear, the sovereignty and territorial integrity of nations, the need for peaceful resolution of disputes,'' said Susan Rice, Obama's national security adviser. ''And we will continue to have that discussion throughout each of the stops on our trip.''
Obama's eight-day Asia swing is a makeup for a visit he canceled last fall because of the U.S. government shutdown. Leaving Washington on Tuesday, he will stop briefly in Oso, Washington state, where mudslides killed dozens of people. He will arrive Wednesday in Japan.
Obama's advisers say there are no plans to scrap the trip if the situation in Ukraine worsens. But the president may have to make decisions while traveling about imposing more penalties against Russia if a deal to ease the crisis collapses.
The U.S., Russia, Ukraine and the European Union signed an agreement Thursday. But already, the prospects of it holding appear slim, with pro-Russian insurgents in eastern Ukraine refusing to leave the government buildings they occupy in nearly a dozen cities.
Russia's foreign ministry on Saturday said it would offer strong help to Ukraine, but that responsibility for reducing tensions rested with Ukrainians, not outsiders.
Compared with Russia's actions in Ukraine, China has been relatively restrained in its territorial ambitions. But tensions spiked last fall when Beijing declared an air defense zone over a large part of the East China Sea, including the disputed islands controlled by Japan and a maritime rock claimed by both China and South Korea. China's coast guard also has blocked Filipino ships in the South China Sea in recent weeks.
China claims virtually the entire South China Sea. Nansha is the Chinese name for the Spratlys, a chain of resource-rich islands, islets and reefs claimed partly or wholly by China, the Philippines, Malaysia and other southeast Asian nations.
Former Philippine national security adviser Roilo Golez said he expects Beijing to avoid Russian-style moves on any of the disputed territories, in large part because China is surrounded by American allies from the East China Sea to the Strait of Malacca and may have to deal with the U.S. military in the region if it undertakes a major act of aggression.
''It would be a folly on the part of China to do anything drastic, to do a Crimea,'' Golez said.
Associated Press writers Jim Gomez in Manila, Philippines, and Elaine Kurtenbach in Tokyo contributed to this report.