 "Asian shares tick higher to five-month high")
The change in expectations followed a 16-day shutdown of the US government that could cloud the economic outlook and make the Fed wary of scaling back its $85 billion-a-month bond-buying programme this year as many had expected. This kept the dollar on the defensive.
Investors face a deluge of US data this week as government departments reopen, with the September nonfarm payrolls report due on Tuesday.
"Such strong readings would again ignite a debate on an imminent start of US tapering, but given that the full impact of the recent shutdown may take some further time to emerge, we continue to see tapering in first quarter next year," analysts at Societe Generale wrote in a note.
Australian shares scaled a five-year peak, also supported by data last week showing an improvement in economic growth in China, its biggest export market.
MSCI's broadest index of Asia-Pacific shares outside Japan inched up 0.1% to a five-month high.
The benchmark S&P 500 US index rose 0.7% on Friday to close at a record high for the second straight day, capping its biggest weekly gain in three months on stronger-than-expected earnings from the likes of Google and Morgan Stanley.
Of the 98 S&P 500 companies that have so far reported quarterly earnings, two-thirds either beat or met market expectations, according to Thomson Reuters StarMine.
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In terms of valuations, the S&P 500's 12-month forward price-to-earnings ratio stood at 13.9, in line with its 10-year average of 14 and slightly above the Nikkei's 13.5 and the pan-European STOXX Euro 600 index's 12.7, data from Thomson Reuters Datastream showed.
Tokyo's Nikkei climbed 1% to a three-week high. It is up 41% this year and its 30-day implied volatility has risen sharply above that in the United States and Europe, Datastream figures showed.
The dollar index, which tracks the greenback against a basket of major currencies, was at 79.707 on Monday, not far from an eight-month low of 79.478 touched on Friday.
The dollar was steady at $1.3673 to the euro after hitting an eight-month low at $1.3704 in the previous session, and down a touch at 98.07 yen.
Barclays Capital analysts said a strong reading in the US jobs data could see markets pare back expectations of a delay in the Fed's tapering, which would lead to a rally in the dollar.
"We forecast nonfarm payrolls to increase by 200,000 and the unemployment rate to decline to 7.2%. Results in line with our forecast would likely lead to a broad US dollar rally, as expectations for a taper delay are pared back," they wrote in a note.
In the commodity markets, Brent crude added 0.1% to be just above $110 a barrel, building on Friday's 0.8% rise. Gold was little changed at around $1,316.5 an ounce.