The euro rose 0.1% to $1.17795, stabilizing after its drop last week to the lowest since early April at $1.1752.
The dollar index, which measures the currency against six major peers, slipped slightly to 92.833 due to pressure from the euro and yen, but was still close to last week's 3-1/2-month high of 93.194.
It has gained nearly 4% from a recent low on May 25 as an improving U.S. economy bolstered the outlook for the Fed to start paring asset purchases as early as this year.
Commonwealth Bank of Australia projects the dollar can continue to strengthen this week on the possibility of the Fed moving a step closer to tapering at the conclusion of its two-day policy meeting on Wednesday.
"We expect the FOMC to drop 'substantial' from 'substantial further progress'," in its guidance on the necessary conditions for the labour market before removing monetary support, CBA strategist Joseph Capurso wrote in a client note.
"Removing 'substantial' will signal the FOMC believes it will soon be appropriate to taper asset purchases," setting up a possible announcement of a taper in September, he said.
The risk to such an outlook is the rise in COVID-19 cases in the United States, coming after the Fed at its last meeting on June 16 dropped a reference to the coronavirus as a drag on the economy.
"Overall, the Fed is expected to hold a rather neutral stance before the Jackson Hole symposium in late August, while risks are biased to dovish side given the Delta variant spread," Mizuho Bank strategist Ken Cheung wrote in a report.
The dollar index eked out a 0.2% gain last week, benefiting from a safe-haven bid on fears a surge in infections of the fast-spreading Delta variant could derail the global recovery, but paring those gains as strong U.S. earnings lifted stocks to record highs.
The risks from the Delta variant continue to rise globally, with top infectious disease official Anthony Fauci saying some Americans may need booster shots amid new mask mandates and a surge in new cases.
China reported its highest number of cases since the end of January, while new infections have also spiked in Japan, where Tokyo is currently hosting the Olympics.
Australia's most populous state of New South Wales, home to Sydney, reported a rise in new COVID-19 cases on Monday despite a weeks-long stay-at-home order.
Meanwhile, MSCI index of Asia-Pacific stocks excluding Japan sank 2% on Monday, as Chinese blue chips slumped 3.8%.
However, cryptocurrencies were buoyed on Monday after London's City A.M. newspaper cited an un-named "insider" on the weekend as saying that Amazon is looking to accept bitcoin payments by year-end.
The report followed Twitter boss Jack Dorsey's comment on Friday that the digital currency is a "big part" of the social-media firm's future.
Bitcoin extended its gains from near $29,000 last week to push back to the cusp of $40,000 on Monday for the first time since mid-June. It last traded about 8.5% higher at $38,455.
Smaller rival ether was last up 6.8% at $2,344.08, recovering from as low as $1,717.17 last week.
(Reporting by Kevin Buckland Editing by Shri Navaratnam and Sam Holmes) ((Kevin.Buckland@thomsonreuters.com;))