Vice President Joe Biden predicted the U.S. and Japan would rebound from their respective problems, describing the two countries’ alliance as “indispensable” to ensuring peace in the Asia Pacific.

He leaves Japan Wednesday and will meet with families at Marine Corps Base Hawaii in Kaneohe on Thursday.

“While you’re struggling to deal with one of the greatest natural disasters any country has faced and we are dealing with getting our budget in order, there are voices in the world who are counting us out,” Biden said yesterday in Tokyo before meeting with Japanese Prime Minister Naoto Kan on the final leg of his Asia tour. “They’re making a very bad bet.”

The visit to Japan follows a four-day trip to China hosted by counterpart Xi Jinping, who is the frontrunner to succeed President Hu Jintao in 2013. Biden said he went to China to build a relationship with Xi and wanted to make clear that the U.S. is a Pacific power and Japan a key ally. The U.S. has about 38,000 service personnel stationed at bases in Japan.

“Without those bases it’s going to be very hard to help manage the successful and peaceful re-rise of China,” said former Deputy Secretary of State Richard Armitage. “Without those bases, because of the tyranny of time and distance, we couldn’t effect meaningful security cooperation.”

Biden underscored Japan’s importance as a strategic ally in Asia, describing the relationship as the “anchor” of U.S. policy in the region.

“This alliance always plays an indispensable role” in ensuring security for the Asia Pacific region, he said later in the day during a visit to the city of Sendai, one of the areas hardest hit by the March 11 magnitude-9 temblor.

“If there was ever a single set of circumstances for the world to understand what the Japanese people are made of” it was “this god awful tragedy that you have had to go through,” Biden told an audience including U.S. soldiers who helped in recovery efforts and families displaced by the disaster.

The earthquake and tsunami knocked out power and cooling at the Fukushima nuclear power plant, about 137 miles north of Tokyo, causing the worst atomic disaster since Chernobyl in 1986.

At a community center, Biden commiserated with families displaced by the quake. “My heart goes out to you,” he said. “Losing a home is only exceeded by losing family.”

The trip is “a statement of solidarity in the wake of the tragedies of March,” said Jeff Bader, who was the senior director for Asian Affairs at the National Security Council until April. “When a senior official goes to China, there’s a desire to demonstrate to the rest of the neighborhood that our presence in Asia is not solely about China.”

Kan thanked Biden for the “enormous” assistance from the U.S. in the wake of the earthquake, adding that his visit was a demonstration “to the world that Japan is open for business.”

More than 20,000 were dead or missing following the earthquake as of Aug. 13, according to Japan’s National Police Agency. The temblor triggered the biggest two-day rout of Japanese stocks since October 1987.

Kan is set to stand down this month, leaving his party to choose a successor who can restore public faith shattered by the nuclear crisis and a procession of five leaders in as many years. His approval rating is below 20 percent over his handling of the March 11 earthquake.

Whoever succeeds Kan will face a country burdened by deflation, an aging population and the world’s largest debt as well as the threat the yen’s rise to a post-war high poses to an export-led recovery.

The government downgraded its growth forecast for Japan this month, saying GDP will increase 0.5 percent in the year started April, compared with its January forecast for a 1.5 percent expansion. The changes reflect the earthquake’s impact on output and consumer spending, the Cabinet Office said.