But the latest data suggested the prolonged trade conflict between Washington and Beijing is taking a further toll on regional growth.
Japan's benchmark Nikkei 225 added 1.6% in morning trading to 21,618.45. Australia's S&P/ASX 200 gained 0.5% to 6,654.70. South Korea's Kospi was marginally higher at 2,131.43. Hong Kong's markets were closed for a national holiday. The Shanghai Composite rose 1.4% to 3,021.65.
Wall Street ended last week on an upbeat note after the Federal Reserve raised expectations that it is prepared to cut interest rates if needed to keep the economy growing.
The S&P 500 index rose 0.6% to 2,941.76. The index ended the month with a 6.9% gain. The Dow Jones Industrial Average gained 0.3% to 26,599.96. The Nasdaq composite rose 0.5% to 8,006.24.
The Trump-Xi meeting in Japan marked the first time the two leaders had met since the dispute over trade and technology escalated following 11 rounds of negotiations.
While the agreement to resume talks forestalls a worsening in the conflict it remains unclear whether there will be a resolution. The last time Trump and Xi met — in early December at a G-20 gathering in Buenos Aires, Argentina — they also reached a cease-fire that injected new life into the talks. But the momentum didn't last.
The trade dispute has led both countries to levy billions of dollars' worth of tariffs on each other's exports, raising concerns over the impact on global economic growth and corporate profits.
"Asia markets will have the trade truce to cheer at the start of the fresh week following the Trump-Xi meeting on Friday," said Jingyi Pan, market strategist with IG in Singapore.
"While a packed data calendar lies ahead in the day, expect the positive glow from the temporary tariffs delay to be the key driver for price movements."
Despite the positive news on the trade front, the latest data were less upbeat.
A closely watched survey by Japan's central bank, released Monday, showed confidence among major manufacturers in the economy worsened for the second straight quarter.
The Bank of Japan's quarterly "tankan" survey of major companies showed confidence deteriorated in June compared with March, with the main index for major manufacturers fell to 7 in June from 12 in the previous quarterly survey in March.
Meanwhile, another indicator, the purchasing managers' index (PMI) for China's manufacturing sector, remained stable but still in contractionary territory at 49.4 in June, even with May's reading, the National Bureau of Statistics reported.
Readings above 50 indicate expansion, while a reading below 50 reflects contraction.
ENERGY: Benchmark crude oil rose $1.21 to $59.62 a barrel in electronic trading on the New York Mercantile Exchange. It fell 96 cents to $58.47 a barrel on Friday. Brent crude, the international standard, rose $1.34 to $66.08 a barrel.
CURRENCIES: The dollar rose to 108.24 Japanese yen from 107.87 yen on Friday. The euro strengthened to $1.1353 from $1.1371.