Analysts said the dollar, which is slipping toward a 15-year low against the yen, could, along with rumblings of geopolitical tensions in the Middle East, continue to bolster oil prices that last week ended above $80 for the first since May.
U.S. crude for September delivery rose 55 cents to $81.25 a barrel by 3:30 a.m. ET. The contract fell $1.31 or 1.6 percent to settle at $80.70 a barrel on Friday, but ended the week 2.2 percent higher.
London Brent crude gained 54 cents to $80.70.
I think technically the market has been on an uptrend for the last couple of weeks, and that's sustained, said Tony Nunan, a risk manager with Mitsubishi Corp in Tokyo. The dollar's weakening is part of why crude has been strong.
Nunan said U.S. crude may try a recent high of $82.97 a barrel hit earlier this month.
The U.S. economy lost 131,000 jobs in July -- more than twice the decline of 65,000 that economists forecast in a Reuters poll. And the closely watched private employment number rose less than expected.
The gloomy data has further weakened the dollar in Asian trade, with the greenback slipping toward a 15-year low against the yen.
Investors will eye China's trade and industrial output data due mid-week to gauge how the country's economy is faring, with the Ministry of Commerce having warned that the second half of the year would be a grim period for its exporters.
Analysts at Australia & New Zealand Bank said reports of escalating geopolitical tension in the Middle East could provide some support to oil prices.
Iran showed off four new domestically made small submarines on Sunday that Tehran said would bolster its defense capability as it vows to confront any military threat from countries opposed to its nuclear program.
In a sign that most investors remain bullish on oil prices, open interest positions remained heavy at the September $85, $90 and $95 call options on Friday, while money managers also increased net long crude oil positions on the New York Mercantile Exchange in the week through August 3.
On the weather front, Tropical Storm Colin weakened to a tropical depression in the Atlantic Ocean on Sunday as it passed west of Bermuda, the National Hurricane Center (NHC) said, adding the system could dissipate later in the day.
(Editing by Michael Urquhart)