Asian equity benchmarks ended the day higher Friday, as news that a potential meeting between North Korean leader Kim Jong Un and President Donald Trump eased some investors’ worries about geopolitical tensions.

But stocks broadly pared their steepest gains late in the session.

South Korea’s Kospi 180721, -0.95% closed 1.1% higher and the won USDKRW, +0.00% rose 0.4% against the dollar. Japan’s Nikkei Stock Average NIK, +0.17% rose as much as 2.4% in morning trading and finished up 0.5%.

During the morning’s push into so-called risk assets like stocks, havens such as the Japanese yen fell in Asia. It was widely down about 0.4% against other major currencies, while U.S. gold futures were had slipped 0.3% and bond yields edged higher. Yields move inversely to prices.

The potential meeting between the U.S. and North Korean leaders, news of which came before most Asian stock markets opened for trading, followed an invitation in a letter from Kim that was delivered to the White House by South Korea’s national-security adviser. Kim reaffirmed that he was prepared to suspend nuclear and missile tests while North Korea engages in talks on the denuclearization of the Korean Peninsula, reducing geopolitical fears among some market participants.

“It’s a complete U-turn,” said Michael Herzum, head of multi asset strategy at Union Investment. While there is still some uncertainty about the meeting’s details, it should reduce geopolitical risk which could potentially help pockets of the market including the Korean won, Japanese and Asian emerging market equities, he said

The meeting would mark the first time a serving U.S. president has sat down with the leadership of the heavily militarized country.

Analysts at Citi said, however, that many “remain skeptical of [a] significant breakthrough” in relations, in light of previous attempts to engage North Korea.

A soft spot in both Japan and Korea was steel stocks, hit by confirmation Thursday that the U.S. will levy tariffs on steel and aluminum. Korea’s Posco’s 005490, -0.52% fell 3.6% and Japan’s JFE 5411, -0.74% declined 1.5%, putting its March decline at 9.7%.

Trump accepts invitation to meet North Korea's Kim Jong Un

Some analysts say the tariff announcement should have less impact than initially feared given both Mexico and Canada have been exempted. Others could also receive exemptions over time. U.S. stocks rallied into the close as firm details were released ahead of the closing bell there, though steel companies there fell more than 2%.

“The tariffs are not as tight as people had feared,” said Michael McCarthy, chief market strategist at CMC Markets. “Tariffs are not a new thing for the U.S. and I think the markets are moving toward seeing this as a [more holey] tariff wall than was expected.”

But Rob Carnell, chief economist and head of research in Asia-Pacific for ING, said the tariffs were “not the end of the story” and that there might be other levies put in place either by the U.S. or other countries in response.

During the morning’s push into so-called risk assets like stocks, havens such as the Japanese yen fell in Asia. It was widely down about 0.4% against other major currencies, while U.S. gold futures were recently down 0.3% and bond yields edged higher; yields move inversely to prices.

In Hong Kong, the Hang Seng Index HSI, -2.06% rose 1.1% and the startup-heavy ChiNext Price Index in China surged a further 3.5%, extending recent outperformance.

The global market’s focus will turn somewhat toward Friday’s U.S. jobs report, with wage growth again to be closely scrutinized for signals of possible future inflation in America.

The Bank of Japan on Friday left its aggressive easing policy unchanged and offered no new clues on when and how it might join other major central banks in winding down its measures as Haruhiko Kuroda heads toward a second five-year term as governor.

— Suryatapa Bhattacharya and Gregor Stuart Hunter contributed to this article.