"The surge in oil prices will also provide a selective opportunity to sell the US dollar against oil-sensitive major currencies," wrote Stephen Innes, chief global markets strategist at AxiCorp.
The Norwegian crown was lifted by rising oil prices, supported by output cuts and signs of a recovery in demand.
Against the dollar, Norway's crown rose more than 1% to 10.0821. The Canadian dollar rose 0.52% to 1.4036.
Other commodity currencies also rose and gold gained more than 0.7%, hovering across its highest in over seven years.
The dollar index, which posted gains of about 0.6% last week, gradually gave up early gains and was down 0.12% at $100.25.
US Federal Reserve Chairman Jerome Powell's willingness to print more dollars and extend the monetary stimulus further to fight the coronavirus economic crisis was welcomed by investors.
Bets against the US dollar shrank to the smallest position in seven weeks in the latest week, according to calculations by Reuters and US Commodity Futures Trading Commission data released on Friday.
Gains in stocks also lifted other major currencies, such as the Australian dollar, which was up half a percent at $0.6446. The euro fell 0.1% to $1.0806.
Against the yen, the US currency fell about 0.25% to 107.30 per dollar after data showed Japan slipped into recession for the first time since 2015. Policymakers are bracing for the nation's worst postwar slump.
Investors were also looking to Purchasing Managers' Index surveys due from major economies later this week for the next insight into the outlook.
The pound took back some ground lost earlier against the euro and was trading at 89.08 pence after a week-long deadlock over a post-Brexit trade deal with the European Union.
Money markets also ramped up expectations of negative interest rates in the United Kingdom for the first time ever as policymakers debated further steps to support the struggling British economy.