While attempting a bounce in Asian and early European trading, by midday in London the greenback had fallen back to its lowest levels since Wednesday .
It gained about 0.2% against the kiwi, which sat at $0.7022, traded 0.2% lower at 110.82 yen JPY= and fell 0.1% to $1.1876 per euro.
U.S. markets are closed on Monday for the Independence Day holiday.
"Friday's NFP jobs report gave something for everyone in terms of an above-consensus NFP gain, but also an above-consensus unemployment rate," strategists at ING said in a note to clients.
"U.S. interest rate markets slightly softened their stance on early Fed tightening and the dollar ended slightly softer. Today's U.S. public holiday suggests trading will be quiet today, although the Fed story will very much re-emerge on Wednesday evening when investors pore through the minutes of the pivotal June 16th FOMC (Federal Open Markets Committee) meeting."
The dollar index was 0.2% lower at 92.154, falling below Friday's levels. But with a 2% rise in the three weeks since the Fed surprised investors with projected hikes in 2023, analysts think the dollar has room to rise a bit further.
"Since the hawkish tilt of the Fed in June, the dollar has been increasingly sensitive to the strength of the domestic data whilst some DM and EM peers still battle COVID outbreaks," analysts at Maybank in Singapore said in a research note.
"As such, this dollar strength can linger a while longer and a sanguine risk climate may not be entirely detrimental for the greenback at this time."
Elsewhere, sterling was 0.2% higher at $1.3860 and emerging market currencies in Asia made small gains to catch up with the dollar's Friday drop.
Traders' focus this week is on minutes from the Fed's June meeting - due Wednesday - and on a meeting of Australia's central bank, both having the potential to rouse currencies from months of range trading amid uncertainty around policy outlook.
"More information on when the FOMC could taper its asset purchases can boost U.S. interest rates and the dollar," said Commonwealth Bank of Australia analyst Joe Capurso, referring to the rate-setting Federal Open Market Committee.
"So can further evidence that the FOMC's outlook for inflation is shifting. In particular, analysts will look for signs that the FOMC is less confident the spike in inflation will be transitory," he said. "Or that the FOMC's tolerance for an inflation overshoot is waning."
Also on the horizon this week is a Reserve Bank of Australia (RBA) meeting on Tuesday, which has markets on tenterhooks because the central bank has flagged a decision on the fate of its bond purchase programme and yield target.
No change to the cash rate is likely, but economists expect the three-year yield target to stay on April 2024 bond - without being extended to the November 2024 bond line, and for the RBA to adopt a flexible approach to bond purchases.
"RBA policy has successfully contained AUD strength despite strong terms-of-trade; but with undervaluation approaching historical extremes, dovish surprises may have less impact on FX," BoFA Global Research analysts said in a note.
Cryptocurrencies were offered on Monday, with bitcoin below its 20-day moving average at $34,256 and ether down 3% at $2,280.
(Reporting by Ritvik Carvalho; additional reporting by Tom Westbrook in Singapore; Editing by Kevin Liffey and Toby Chopra) ((Ritvik.Carvalho@thomsonreuters.com; +44 2075429406; Reuters Messaging: firstname.lastname@example.org; Twitter @ritvikcarvalho))