BANGKOK — Asian shares rallied and U.S. futures jumped Monday, with Japan’s benchmark Nikkei 225 topping 50,000 for the first time.

Work on trade deals that might alleviate friction between the U.S., China and other major trading partners contributed to upbeat sentiment as U.S. President Donald Trump visited Malaysia for a summit of Southeast Asian nations where he reached preliminary trade agreements with Malaysia, Thailand, Cambodia and Vietnam.

A trade deal between the United States and China was drawing closer, officials from the world’s two largest economies said Sunday as they reached an initial consensus for Trump and Chinese leader Xi Jinping to try to finalize during a high-stakes meeting later in the week.

“This isn’t just photo-op diplomacy. Behind the showmanship, Washington and Beijing’s top trade lieutenants have quietly mapped out a framework that might, just might, keep the world’s two largest economies from tearing up the field again,” Stephen Innes of SPI Asset Management said in a commentary.

Trump was heading next to Japan before ending his Asian tour in South Korea where he is expected to meet with Xi on the sidelines of a Pacific Rim summit, the Asia-Pacific Economic Cooperation (known as APEC) forum.

A report by the APEC secretariat released Monday forecast that annual growth in the region circling the Pacific will slow to 3% this year from 3.6% last year, partly due to trade restrictions and higher tariffs.

In Japan, opinion polls showed newly installed Prime Minister Sanae Takaichi enjoying high levels of public support for her market-friendly policies. The Nikkei 225 gained 2.1% to 50,329.08, hitting record intraday highs.

Takaichi is Japan’s first female prime minister. She favors raising defense spending and that has boosted prices of stocks in major defense contractors, such as Kawasaki Heavy Industries, which gained 8.7%. IHI Corp. jumped 2.6% and Hitachi gained 2.7%.

Trump has long complained American cars were shut out Japanese markets, one of various reasons he cited for imposing tariffs of 25%, then lowered to 15%, on American’s most vital ally in Asia. So Japan’s government has floated the idea of buying a fleet of Ford F-150 trucks to use to inspect roads and infrastructure.

Shares jumped in South Korea, where the Kospi was up 2% at 4,018.73, also a record. Investors there are hoping for a trade deal with Trump.

Chinese markets likewise saw solid gains. Hong Kong’s Hang Seng rose 1% to 26,427.34, while the Shanghai Composite index added 1% to 3,991.35.

In Australia, the S&P/ASX 200 picked up 0.3% to 9,047.40.

Taiwan’s Taiex gained 2.1% and the Sensex in India was up 0.5%.

On Friday, U.S. stocks hit records after an update on inflation came in a bit less painful than feared.

The S&P 500 rose 0.8% to 6,791.69, topping its prior all-time high set earlier this month. The Dow Jones Industrial Average rallied 1% to 47,207.12, also a record.

The Nasdaq composite climbed 1.1% to a record of 23,204.87.

The data on inflation was encouraging because it could mean less pain for lower- and middle-income households struggling with still-high increases in prices. Even more importantly for Wall Street, it could also clear the way for the Federal Reserve to keep cutting interest rates in hopes of giving a boost to the slowing job market.

The Fed just cut its main interest rate last month for the first time this year, but it’s been hesitant to promise more relief because lower rates can make inflation worse, beyond goosing the economy and prices for investments.

Most big U.S. companies are reporting stronger profits for the latest quarter than analysts expected, also raising hopes for steady growth.

In other dealings early Monday, U.S. benchmark crude oil gained 15 cents to $61.65 per barrel. Brent crude, the international standard, was up 12 cents at $65.32 per barrel.

The U.S. dollar rose to 153.15 Japanese yen from 152.85 yen. The euro slipped to $1.1622 from $1.1636.