The euro slid on Thursday despite a record interest rate hike by the European Central Bank as US Fed chief Jerome Powell made hawkish comments.
Meanwhile, the pound remained close to a 37-year low against the dollar that was struck Wednesday, as new British Prime Minister Liz Truss announced that she will freeze domestic fuel bills for two years to help ease the burden of a UK cost-of-living crisis.
The ECB warned Thursday that inflation was "far too high" and likely to stay above target for "an extended period" as it announced its record 0.75 percentage point hike.
ECB chief Christine Lagarde made clear interest rates were far from where they need be to bring inflation down.
"We actually took the decision today that we would continue to raise interest rates... because we believe that we are far away from the rate at which we hope we'll see inflation return to the two percent medium term target," she said.
Lagarde also warned the eurozone risks recession if Russia completely cuts off gas, which it has nearly done.
But comments by Fed chief Jerome Powell were seen as even more hawkish than those by Lagarde.
"We need to act now forthrightly, strongly as we have been doing and we need to keep at it until the job is done to avoid ... the kind of very high social costs" of the surge in inflation in the 1970s and 1980s, Powell told a US think tank.
- Greenback 'more attractive' -
Chris Beauchamp, chief market analyst at online trading platform IG, said "Investors clearly believe that the Fed is more committed to higher rates than the ECB, while the stronger economic performance of the US means the greenback and not the euro seems the more attractive prospect."
The euro, which had broken back above parity with the dollar, slid down as far as $0.9934 before recovering some ground.
The Fed has made it clear it plans to continue to aggressively raise interest rates to rein in surging inflation, even at the cost of causing some economic pain.
The dollar has moved ever higher against its major peers in recent weeks as investors flood into the currency hoping for better returns as the Fed raises rates and as they seek a haven in the face of economic turmoil.
The euro on Wednesday touched a fresh 20-year dollar low.
The US unit is closing in on a 32-year peak against the yen owing to the Bank of Japan's refusal to raise interest rates.
Observers expect the dollar to keep attracting strong interest as long as the Federal Reserve keeps ramping up US interest rates by sizeable amounts.
The Fed holds its next policy meeting on September 21, with a third successive 75-basis-point lift forecast.
In equities trading, eurozone stocks closed the day mostly higher, and Wall Street was also up in morning trading.
"It has been slow going, but stocks look like they are in a mood to continue yesterday’s rebound," said IG's Beauchamp.
"The selling of late August and early September seems to have been exhausted for now, although the broader outlook is still less than encouraging," he added.
- Key figures at around 1530 GMT -
New York - Dow: UP 0.5 percent at 31,736.76 points
EURO STOXX 50: UP 0.3 percent at 3,512.38
London - FTSE 100: UP 0.3 percent at 7,262.06 (close)
Frankfurt - DAX: DOWN less than 0.1 percent at 12,904.32 (close)
Paris - CAC 40: UP 0.3 percent at 6,125.90 (close)
Tokyo - Nikkei 225: UP 2.3 percent at 28,065.28 (close)
Hong Kong - Hang Seng Index: DOWN 1.0 percent at 18,854.62 (close)
Shanghai - Composite: DOWN 0.3 percent at 3,235.59 (close)
Euro/dollar: DOWN at $0.9960 from $1.0012 on Wednesday
Pound/dollar: DOWN at $1.1492 from $1.1535
Euro/pound: DOWN at 86.66 pence from 86.74 pence
Dollar/yen: UP at 143.94 yen from 143.79 yen
West Texas Intermediate: UP 1.7 percent at $83.29 per barrel
Brent North Sea crude: UP 1.0 percent at $88.87 per barrel