Benchmarks in Shanghai, Tokyo, Hong Kong and Sydney all climbed.
Traders were encouraged by U.S. Treasury Secretary Steven Mnuchin's suggestion last week that trade envoys might meet in person following two rounds of phone conversations. Mnuchin gave no timeline, but his comments helped to temper anxiety over U.S.-Iranian tensions.
Traders have focused on signs of movement toward a settlement of the U.S.-China tariff war over Beijing's technology ambitions.
They were reassured by an agreement in June by Presidents Donald Trump and Xi Jinping to resume stalled talks. That is despite warnings the truce is likely to be fragile because the two sides are divided by the same array of disagreements that caused negotiations to collapse in May.
The Shanghai Composite Index rose 0.4% to 2,898.20 and Tokyo's Nikkei 225 climbed 1% to 21,620.88. Hong Kong's Hang Seng advanced 0.3% to 28,450.32 and Seoul's Kospi was 0.4% higher at 2,101.45. India's Sensex edged up 0.1% to 38,065.10.
Sydney's S&P-ASX 200 gained 0.5% to 6,724.60. New Zealand and Taiwan climbed while Southeast Asian markets retreated.
Investors also looked ahead to this week's meeting of European Central Bank and the U.S. Federal Reserve next week.
"Reports of the U.S. and China resuming trade negotiations next week are positive for risk sentiment, but escalating tensions in the Middle East pushing oil higher are negative," said ING in a report. "We anticipate wait and watch sentiment" ahead of the ECB and Fed meetings.
On Wall Street, the benchmark Standard & Poor's 500 index rose 0.3% to 2,985.03. The index is back within 1% of its record, set a week earlier.
The Dow Jones Industrial Average edged up 0.1% to 21,171.90. The Nasdaq composite rose 0.7% to 8,204.14.
Apple, Intel and several chip makers jumped more than 2% and technology stocks in the S&P 500 climbed 1.2%. But the other 10 sectors that make up the index were evenly split between gainers and losers, and none moved by more than 0.5%.
Earnings reports are due over the next two weeks from about three-fifths of S&P 500 companies. Expectations are generally modest.
Slowing global economic growth and rising costs are weighing on companies. Many investors are more interested in what CEOs say about how Trump's trade war will affect profits than in their results for the spring.
Markets also are watching tensions over Iran's nuclear program.
Washington announced sanctions this week on a Chinese oil company, Zhuhai Zhenrong, that it said violated controls on transporting Iranian crude. Beijing has said it supports nuclear nonproliferation efforts but rejects unilateral U.S. sanctions.
"This simultaneously turns U.S. pressure up on Iran and also stresses the already strained U.S.-China relations," Mizuho Bank said in a report.
There is a "significant risk of a longer-term shift toward a more hawkish stance on the Iran issue" if Boris Johnson becomes the British prime minister as expected, Stephen Innes of Vanguard Markets said in a report.
"The U.S. administration will waste little time pressuring the new UK PM to toe a stricter line on the nuclear accord."
ENERGY: Benchmark U.S. crude gained 20 cents to $56.42 per barrel in electronic trading on the New York Mercantile Exchange. The contract rose 46 cents on Wednesday to close at $56.22. Brent crude, used to price international oils, advanced 30 cents to $63.56 in London. It gained 79 cents the previous session to $63.26.
CURRENCY: The dollar gained to 108.16 yen from Wednesday's 107.86 yen. The euro slipped to $1.1190 from $1.1209.