Joel Kruger, currency strategist at LMAX Group, said the risk-averse mood and inflation fears were joining forces to push the dollar higher.
"It’s becoming increasingly difficult for the Fed to be able to reconcile its stance that inflation is transitory. At some point the definition of transitory is called into question," he said.
Kruger expects more dollar strength in the third quarter, with the dollar index heading towards 96 to 97.
The Australian dollar, seen as a liquid proxy for risk appetite, fell to its lowest since November in early trading before recovering somewhat. At 1124 GMT, it was down 0.2% on the day at $0.73135, while the New Zealand dollar was up 0.1% at $0.6924.
Australia's two largest states reported sharp increases in new COVID-19 cases on Wednesday, a blow to hopes that lockdown restrictions would be lifted as more than half the country's population was subject to stay-at-home orders.
The British pound, which on Tuesday hit its lowest since February, was down 0.1% at $1.3616.
Analysts pointed to a stand-off between Britain and the European Union. Prime Minister Boris Johnson said that his government would outline its approach on the Northern Ireland Protocol to Britain's parliament on Wednesday. COVID-19 cases in Britain are also surging.
The euro was down 0.4% versus the commodity-dependent Norwegian crown, with the pair changing hands at 10.5722 compared to 10.7038 in the previous session, a seven-month low for the crown.
"Generally, we see the recent dip in cyclical FX as a correction rather than a more pronounced trend and look for a recovery in higher beta currencies backed by hawkish central banks later this summer," wrote ING strategists in a note to clients.
Currency markets are looking ahead to the European Central Bank's (ECB) meeting on Thursday. A dovish tone is expected after ECB President Christine Lagarde foreshadowed a guidance tweak in an interview last week.
The euro was down 0.1% against the dollar, at $1.1772, having earlier hit a 3.5-month low.
The ECB announced a new strategy which allows the bank to tolerate inflation above its 2% target, and Lagarde said policy guidance would be revisited to demonstrate the bank's commitment to the new goal.
In cryptocurrencies, bitcoin rose back above $30,000, having dipped below this key level for the first time in a month on Tuesday. At 1129 GMT, it was trading around $31,441, while ether was at $1,902.
(Reporting by Elizabeth Howcroft Editing by Joe Bavier, Kirsten Donovan) ((Elizabeth.Howcroft@thomsonreuters.com; +44 02075427104;))