Many analysts think the Fed will be wary of scaling back its $85 billion-a-month bond-buying programme until the economic impact of a 16-day partial shutdown of the U.S. government is clearer. This kept the dollar on the defensive.
Investors face a deluge of U.S. data this week as reopened government departments catch up with their work, with September nonfarm payrolls report on Tuesday seen as the most important.
U.S. employers are forecast to have added 180,000 workers last month, with the unemployment rate steady at 7.3 percent, a Reuters poll showed.
"Such strong readings would again ignite a debate on an imminent start of U.S. 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, who forecast employment would rise by 240,000, 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 0.2 percent to a five-month high.
In New York, the benchmark S&P 500 index rose 0.7 percent on Friday to close at a second-straight record high, 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.
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 advanced 0.8 percent to a three-week high in relatively light trade. It is up 41 percent this year, spurred by fiscal and monetary stimulus, 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 79.676 on Monday, not far from an eight-month low of 79.478 touched on Friday.
The dollar was steady at $1.36775 to the euro after hitting an eight-month low at $1.3704 in the previous session, and up a touch at 97.77 yen.
Barclays Capital analysts said a strong reading in the U.S. 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 percent. Results in line with our forecast would likely lead to a broad U.S. 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 percent to be just above $110 a barrel, building on Friday's 0.8 percent rise.
Gold gained 0.2 percent to around $1,318.7 an ounce, having posted its best weekly rise in two months last week.