Abe will be the first Japanese leader to address both houses of Congress when he speaks on Wednesday. The prime minister's visit also falls ahead of the 70th anniversary of the atomic bombing of Hiroshima and Nagasaki in August.
Analysts are listening for Abe's remarks on the Trans-Pacific Partnership (TPP), a free trade proposal with major Asia-Pacific nations and the United States that is a decade in the making. China is not part of the deal, which requires participant nations to uphold regulations in intellectual property and other areas.
At a news conference Tuesday with President Barack Obama, Abe said significant progress was made in the trade talks.
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The next step in formalizing the Asia-Pacific trade agreement is congressional approval for the trade promotion authority (TPA), which would give Obama the power to "fast track" the agreement through Congress. It has advanced through a subcommittee.
John Vail, chief global strategist of Tokyo-based Nikko Asset Management, said he expects the Trans-Pacific Partnership to pass in June or July. The Japanese themselves are less optimistic, according to observations by chief economists and strategists for foreign firms in Japan, Vail said. As a result, approval of the trade deal "would be a very positive surprise."
The Nikkei closed up 0.4 percent on Tuesday, topping the psychologically key level of 20,000, which the index reached last week for the first time in 15 years.
The gains came despite the country's disappointing March retail sales report, and ahead of the Bank of Japan's meeting on Thursday. The central bank is likely to remain in easing mode for several more months.
Regardless of monetary or economic developments, technical analysis shows the Nikkei will likely continue its upward climb.
"The NKY still has the support of positive intermediate and long-term momentum," said Katie Stockton, chief technical strategist at BTIG. "For three months, it has taken only one step back for every three steps forward."
She added "there are no signs of exhaustion" and that the next resistance level is the 2000 high of 20,833, with support in the 19,000 area.
Analysts also see fundamental support for the Nikkei from corporate reform that has caused Japanese firms to boost buybacks and dividends, which still lag behind those of their Asian counterparts and U.S. companies.
"There are positive things going on within the Japanese economy, especially on the reform front," said Robin Anderson, senior economist at Principal Global Investors.
Compared to Chinese stocks, which are also at multiyear highs, the rally in Japan is supported by far more institutional investors than in China, said Tai Hui, chief market strategist in Asia for JPMorgan Funds.
He noted that investors in the Chinese stock market are about 70 percent retail and 30 percent institutional, while the ratio is reversed for Japan.