Fed Governor Lael Brainard echoed those comments on Friday, saying "employment has some distance to go."
The dollar index last month hit its highest since the start of April at 93.194 as traders positioned for a start to tapering as soon as this year.
Dollar net long positions rose to their highest level since early March of last year in the week to July 27, according to Reuters calculations and the latest data from the Commodity Futures Trading Commission.
Economists in a Reuters poll forecast a 926,000 job increase in July's non-farm payrolls number, due Friday, which would be the biggest increase for 11 months. The U.S. unemployment rate is forecast to fall to 5.7%, from 5.9% in June.
"The U.S. payrolls will be a marquee event risk," Chris Weston, head of research at broker Pepperstone, wrote in a note to clients.
"If we do see the elusive 1 million jobs created, then calls for a September announcement for tapering the asset-purchases program will ramp up," buoying the dollar, whereas a print of around 703,000 or lower would push the currency lower, he said.
The dollar was little changed at 109.67 yen on Monday, and slightly weaker at $1.1873 per euro.
National Australia Bank predicts the euro could rise toward $1.20 before pushing even higher as euro-area growth quickens amid an accelerating vaccination drive.
"As the euro zone economy picks up relative to the U.S., we should start to see the euro in particular starting to improve," Ray Attrill, NAB's head of forex strategy, said in a podcast for clients.
"EU recovery fund spending is due to start kicking in soon, at the same time that U.S. fiscal support is going to be waning."
Sterling rose 0.11% to $1.39105, with a policy announcement by the Bank of England due on Thursday.
The Aussie dollar was flat at $0.7347 before the Reserve Bank of Australia (RBA) meets on Tuesday, when it is widely expected to backtrack on a previous decision to taper stimulus, with protracted COVID-19 lockdowns dragging on growth.
In cryptocurrencies, bitcoin slipped 0.36% to trade below $40,000, after sliding 5.67% over the weekend.
Smaller rival ether experienced opposite fortunes, holding gains from the weekend to trade around $2,550. It climbed as high as $2,699 on Sunday for the first time in almost two months, up from as low as $1,717.17 less than two weeks ago.
(Reporting by Kevin Buckland; Editing by Sam Holmes and Jacqueline Wong) ((Kevin.Buckland@thomsonreuters.com;))