Tokyo eased 0.12 percent, Hong Kong gave up 0.55 percent, Shanghai was flat and Seoul lost 0.27 percent but Sydney edged up 0.40 percent.
"Market participation levels are likely to remain low until data can help confirm the state of the US economic recovery," said Hiroichi Nishi, SMBC Nikko Securities general manager of equities.
With last week's global rally -- fuelled by the US deal to reopen the government after 16 days and avert a devastating default -- out of the way, attention has turned back to economic results, with the non-farm payrolls in focus.
The figures had been due out at the beginning of the month but were put off because of the US government shutdown. Traders will pore over the results for clues about the state of the economy.
However, Kathy Lien, managing director at BK Asset Management, said there would likely be a cautious reaction to a strong report because it predates the shutdown, which likely depressed hiring.
She added that if jobs growth misses expectations, "the dollar could be in even more trouble because October payrolls are expected to be much weaker".
Economists say there is a good chance the US Federal Reserve will hold off winding down its stimulus programme -- which depressed the value of the dollar -- until possibly the new year.
On currency markets, the dollar was changing hands at 98.23 yen in early exchanges compared with 98.15 yen in New York on Monday, while the euro fetched $1.3671 and 134.28 yen compared with 1.3681 and 134.26 yen.
Wall Street was unable to provide a strong lead as investors took a breather from last week's strong gains.
The Dow was flat and the S&P 500 edged up marginally to another record high, while the tech-rich Nasdaq added 0.15 percent.
In oil trade, New York's main contract, West Texas Intermediate (WTI) for delivery in November, was down 17 cents at $99.05 a barrel in morning trade, while Brent North Sea crude for December gained nine cents to $109.73.
Gold cost $1,314.34 at 0220 GMT compared with $1,315.41 on Monday.