In U.S. trading on Monday, EUR/USD was up 0.28% at 1.3258.
The greenback, meanwhile, was up against the pound, with GBP/USD trading down 0.27% at 1.5560.
Standard & Poor’s earlier revised its long-term outlook on the U.S. credit rating to stable from negative.
The agency affirmed the country's AA+/A-1+ rating.
"The stable outlook indicates our appraisal that some of the downside risks to our ‘AA+’ rating on the U.S. have receded to the point that the likelihood that we will lower the rating within the next two years is less than one in three," Standard and Poor's said.
"We do not see material risks to our favorable view of the flexibility and efficacy of U.S. monetary policy. We believe the U.S. economic performance will match or exceed its peers’ in the coming years. We forecast that the external position of the U.S. on a flow basis will not deteriorate."
The news boosted expectations for the Federal Reserve to begin scaling back stimulus measures soon now that the economy appears to be improving, which supported the dollar earlier.
Stimulus measures, such as the Fed's USD85 billion monthly bond-buying program, weaken the dollar to spur recovery.
The dollar continued to see support from Friday's jobs data before profit taking cooled the greenback's advance.
The Bureau of Labor Statistics said the U.S. economy added 175,000 jobs in May, beating expectations for an increase of 170,000, after 149,000 jobs were created the previous month.
The headline U.S. unemployment rate ticked up to 7.6% last month, from 7.5% in April as more individuals entered the labor market and began fresh job searches.
Meanwhile in France, industrial output rose 2.2% in April from March, beating market calls for a 0.3% gain, which gave the euro support.
The dollar was up against the yen, with USD/JPY up 1.23% at 98.73, and down against the Swiss franc, with USD/CHF trading down 0.29% at 0.9332.
The yen traded lower as investors looked ahead to the outcome of the Bank of Japan’s policy meeting on Tuesday after the bank left policy on hold last month.
Revised data on Monday showed that the Japanese economy expanded by 1.0% in the first quarter, up from a preliminary estimate of 0.9%.
A separate report showed that the country posted a wider-than-predicted current account surplus in April, as a weaker yen boosted the value of income stemming from overseas investments.
The dollar was mixed against its cousins in Canada, Australia and New Zealand, with USD/CAD down 0.07% at 1.0190, AUD/USD down 0.25% at 0.9468 and NZD/USD trading up 0.25% at 0.7899.
The dollar index, which tracks the performance of the greenback versus a basket of six other major currencies, was down 0.03% at 81.91.