"The alliance that we have is the cornerstone of security in East Asia, it is one that my administration wants to strengthen," Obama told reporters before the talks.
"It is for that reason that the prime minister is the first foreign dignitary to visit me here in the Oval Office," he said, adding that the meeting was "testimony to the strong partnership between the United States and Japan".
For his part Aso, battling his country's worst economic slump in more than three decades, said the US and Japan would have to work together to combat the global economic crisis.
"We will have to work together hand-in-hand," he said.
"The most important thing is to maintain confidence in the dollar as a key currency. If confidence in the dollar is damaged it will have a huge affect."
The value of the dollar has risen in the last six months as investors flee emerging markets and stocks, but Japanese leaders remain worried about the yen's persistent strength in global currency markets.
Any weakening of the dollar versus the Japanese currency would further dampen already rapidly shrinking demand for Japanese exports.
North Korea missile
Aso and Obama also agreed to step up efforts to persuade North Korea to abandon its weapons programmes and avoid doing anything provocative.
|Speculation is mounting that North Korea is preparing for a long-range missile test [AFP]
Earlier North Korea said it was preparing to launch a "satellite" into space, a move US and Japanese intelligence agencies believe is actually a test of a long-range missile.
"Regarding the missile issue, we discussed how the initial reactions are important," Aso told reporters after the talks.
"After a missile is launched, we discussed that what is important is how other, foreign nations would act."
A senior Japanese official who attended the talks said the two leaders did not want North Korea to act provocatively.
"In light of North Korea's announcement that it was preparing to launch a satellite on a rocket, the two leaders agreed that North Korea should not take actions that may increase tension," the Japanese official said.
In a separate announcement, officials accompanying Aso said Japan would soon appoint a special envoy on Pakistani and Afghan affairs to join US efforts to bring stability to the region.
An unnamed official told the AFP news agency that Motohide Yoshikawa, the Japanese ambassador to Spain, would shortly be appointed to the post and would then visit Richard Holbrooke, the US special envoy to the region.
"President Obama expressed his gratitude for the assistance Japan provided [for Pakistan and Afghanistan] and said he would welcome Japan's continued active roles in this area," the official said.
Obama's invitation to Aso to be the first foreign leader to visit the White House has been seen as an effort to reassure Japan, which is sensitive about its status as Washington's key ally in Asia.
The change of administration in Washington has led to speculation among Japanese officials that the US may be moving closer to the rising power of China at the expense of its alliance with Japan.
Tuesday's meeting brought together leaders with contrasting political fortunes - Obama is currently enjoying worldwide popularity, but Aso is struggling to stay in power.
With Japan's economy sliding into its worst recession in 50 years, the Japanese prime minister is facing single-digit approval ratings and appeals from his own party to resign.
His administration reached a new low point last week when his finance minister resigned after appearing to be drunk during a world finance ministers' meeting in Rome.