And the dollar weakened on growing expectations for more interest rate cuts, while eyes were on US Presiident Donald Trump's signature tax-cutting bill -- now inching towards a Senate vote -- that some experts warn could add trillions of dollars to the national debt.
The S&P 500 and Nasdaq finished at all-time peaks Friday amid optimism governments will be able to avoid swingeing tariffs imposed by the US president in April and paused until July 9 to allow for negotiations.
Officials from Japan and India have extended their stays in Washington to continue talks, raising hopes for agreements with two of the world's biggest economies.
Hopes that the deadline could be extended were boosted Friday by Treasury Secretary Scott Bessent, who told Fox Business "we have countries approaching us with very good deals" but they might not all be finalised by next week.
But he added: "If we can ink 10 or 12 of the important 18 -- there are another important 20 relationships -- then I think we could have trade wrapped up by Labor Day," which falls on September 1.
Trump said at the weekend that he did not expect to extend the deadline, telling the "Sunday Morning Futures with Maria Bartiromo" show: "I don't think I'll need to".
"I could, no big deal," he added in the interview that was taped Friday.
Meanwhile, Canadian Finance Minister Francois-Philippe Champagne said Sunday that Ottawa would rescind taxes impacting US tech firms in hopes of reaching a trade agreement with Washington after Trump called off talks in retaliation for the levy.
Negotiations would resume with the aim of getting a deal by July 21, Ottawa added.
After Wall Street's record day, most markets mostly followed suit Monday.
Tokyo extended its recent rally fuelled by tech firms, while there were also gains in Shanghai, Sydney, Seoul, Singapore, Wellington, Manila, Bangkok and Jakarta.
US futures also rose but Hong Kong, Mumbai and Taipei fell.
London and Paris was flat while Paris edged down in early trade.
There was little major reaction to data showing the contraction in Chinese factory activity eased further in June after a China-US trade truce.
The dollar extended losses against its peers as traders increased bets on at least two rate cuts this year following Trump's indication he could choose a successor to Federal Reserve boss Jerome Powell within months.
"Markets... are already pricing not just two Fed cuts this year, but a full-blown easing cycle stretching deep into 2026," said SPI Asset Management's Stephen Innes.
"Powell may still hold the gavel, but traders are betting the next Fed chair walks, talks, and cuts like a dove in MAGA red."
However, Ronald Temple, chief market strategist at Lazard, warned: "Were President Trump to announce his nominee to succeed Jay Powell much earlier than usual, it could create a situation where the candidate's commentary could undermine market confidence in the future direction of Fed policy if he or she were to diverge publicly from Fed communications."
Senators were also debating Trump's "One Big Beautiful Bill", which extends his expiring first-term tax cuts at a cost of $4.5 trillion and beefs up border security.
The Republican president has ramped up pressure to get the package to his desk by July 4, and called out wavering lawmakers from his party.
However, there are worries about the impact on the economy, with the nonpartisan Congressional Budget Office estimating the measure would add nearly $3.3 trillion to US deficits over a decade.
- Key figures at around 0810 GMT -
Tokyo - Nikkei 225: UP 0.8 percent at 40,487.39 (close)
Hong Kong - Hang Seng Index: DOWN 0.9 percent at 24,072.28 (close)
Shanghai - Composite: UP 0.6 percent at 3,444.43 (close)
London - FTSE 100: FLAT at 8,796.66
Euro/dollar: UP at $1.1733 from $1.1718 on Friday
Pound/dollar: UP at $1.3723 from $1.3715
Dollar/yen: DOWN at 144.07 yen from 144.68 yen
Euro/pound: UP at 85.58 pence from 85.43 pence
West Texas Intermediate: DOWN 0.2 percent at $65.40 per barrel
Brent North Sea Crude: DOWN 0.1 percent at $67.72 per barrel
New York - Dow: UP 1.0 percent at 43,819.27 (close)
dan/dhw
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