Among other currencies, the South Korean won KRW=KFTC gained 0.4% and the Taiwanese dollar TWD=TP rose 0.2%.
The dollar index =USD, which tracks the US currency against six major peers, was steady after gaining more than 1% last week following the Fed's rate hike, as the central bank signalled more increases could be coming.
Bank Indonesia meeting and rupiah in focus
Investors also awaited Bank Indonesia's (BI) policy meeting this week, looking for clues on the interest rate outlook as policymakers balance currency stability with efforts to support economic growth.
"Inflation is off its back, but still within the BI's target range. Against this backdrop and despite the US Fed's hike, we expect Indonesia's policymakers to exhibit limited urgency to tighten policy at this juncture," said Radhika Rao, senior economist at DBS.
"New Governor Destry (Damayanti) is likely to highlight tighter global financial conditions and geopolitical risks as key risks of the horizon, while the domestic economy continues to be relatively resilient."
The rupiah IDR=, one of the worst-performing currencies in the region so far this year, has appreciated more than 2% since hitting a record low on June 8.
Perry Warjiyo's unexpected resignation as BI chief in July spooked investors. However, the appointment of senior deputy governor Destry as the central bank's first female chief has helped reassure markets and supported a modest recovery in the rupiah.
The rupiah fell 0.4% on Monday, hitting a one-month low.
Trump-Xi summit and Vietnam index inclusion
The Trump-Xi summit in Washington on September 24 is in focus, with markets hoping for signs of improving ties between the world's two largest economies after months of trade and geopolitical tensions.
"Investors are cautiously hoping for the current trade truce to be maintained," said Lukman Leong, analyst at Doo Financial Futures, a brokerage.
"A constructive outcome could provide further support to Asian markets, while renewed trade tensions could weigh on sentiment."
Elsewhere, Vietnamese stocks were added to FTSE Russell's emerging market indexes on Monday, marking a milestone for the country's stock market after years of reforms aimed at attracting foreign investors.
The stock index .VNI rose as much as 0.8%.
Asian tech and chip stocks lead regional gains
Emerging Asian stocks rose on Monday, led by chip-related shares, as investors awaited a meeting between US President Donald Trump and Chinese President Xi Jinping later this week for signals on trade ties and the global economic outlook.
Technology shares drove gains across the region, with South Korea's KOSPI .KSII rising as much as 1.7% to its highest level since September 10.
Taiwanese equities .TWII climbed 1%, touching their highest in nearly three months.
Improving risk appetite for AI and semiconductor stocks lifted North Asian markets, with investors extending bets on chipmakers after gains among their US peers and signs of resilient demand for technology.
Stocks in Singapore .STI rose 0.3%, while Philippine .PSI shares gained 0.2%.
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