At 0808 GMT, the dollar index was up less than 0.1% on the day, at 92.658, having hit its highest since November 2020, at 92.697, overnight.
"The dollar index (DXY) has just broken the 200 day moving average," said James Athey, investment director at Aberdeen Standard Investments, adding that the dollar's next move would be crucial.
The euro was down 0.1% against the dollar, at $1.1807.
On Wednesday, U.S. Treasury Secretary Janet Yellen and Federal Reserve Chair Jerome Powell expressed their confidence in the U.S. recovery during a second day of testimony to Congress.
Stephen Gallo, European head of FX strategy at BMO Capital Markets, wrote in a note to clients that he expected the euro to fall to $1.16 over the next one month.
"The EU's 'third COVID wave', the relatively low vaccine take up rate, and a more subdued fiscal impulse will probably cause the Eurozone's recovery to lag North America's by 2-3 months," Gallo wrote.
"The ECB's desire to cap yields is evidence that even a moderate re-pricing of European sovereign debt is a source of systemic risk," he added.
Gallo also said that the handling of the vaccine rollout in Europe, and "resultant forms of protectionism" could permanently deter investors.
European leaders meet at a summit later on Thursday and are likely to discuss vaccine supply issues. The EU on Wednesday tightened its oversight of coronavirus vaccine exports, giving it greater scope to block shipments to countries with higher inoculation rates such as Britain.
The Swiss National Bank kept its ultra expansive monetary policy in place, including the world's lowest interest rate, saying that the Swiss franc remains "highly valued".
"The fact that the Swiss banks’ sight deposits have been reasonably stable since the autumn suggests that the central bank has largely withdrawn from the FX market," wrote Commerzbank strategist Thu Lan Nguyen.
However, Nguyen said that she would not rule out the possibility of further SNB interventions in the FX market to limit possible future franc appreciation.
At 0828 GMT, the franc was down around 0.1% against the euro at 1.1068.
The Aussie and Kiwi dollars were a touch higher, both up around 0.3% against the U.S. dollar, recovering some of their losses from the previous two sessions.
Elsewhere, bitcoin was little changed at around $52,321.31.
The cryptocurrency briefly topped $57,000 in the previous session after Tesla Inc boss Elon Musk said customers can now buy the company's electric cars with the digital token.
(Reporting by Elizabeth Howcroft. Editing by Jane Merriman) ((Elizabeth.Howcroft@thomsonreuters.com; +44 02075427104;))