The greenback has come under pressure recently as the U.S.-China trade war threatens to derail global economic growth, adding to bets that the Federal Reserve is closer to cutting interest rates.
A sustained decline against the euro has not yet emerged, however, as the U.S. currency still benefits from relatively higher rates than in Europe.
"You still have a very large divergence between the Federal Reserve and the European Central Bank, and that's really what's precluding a sustained euro/dollar rally based on the expectations of what the Fed's going to do going forward," said Bipan Rai, North American head of FX strategy at CIBC Capital Markets in Toronto.
The dollar was boosted on Wednesday after Trump said that he had a "feeling" that a U.S.-China trade deal could be reached, though he again threatened to increase tariffs on Chinese goods if no agreement is reached.
The euro dropped as Trump said he was considering sanctions over Russia's Nord Stream 2 natural gas pipeline project and warned Germany against being dependent on Russia for energy.
The dollar briefly fell earlier on Wednesday after the U.S. Labor Department said its consumer price index edged up 0.1% last month. Excluding the volatile food and energy components, the core CPI nudged up 0.1% for the fourth straight month.
The next major economic indicator will be Friday's retail sales data for May.
The Fed is not widely expected to cut rates when it meets on June 18-19, though investors will be watching for any new signals that a cut is getting nearer.
Interest rate futures traders are now pricing in a 21% chance of a cut in June and an 85% likelihood of at least one cut in July.
Investors are also nervous that trade battles will spread to Japan and Europe, with Trump on Tuesday accusing Europe of devaluing the euro zone's single currency.
"The Euro and other currencies are devalued against the dollar, putting the U.S. at a big disadvantage," Trump wrote on Twitter.
Sterling also dropped on Wednesday after British lawmakers defeated an attempt led by the opposition Labour Party to try to block a no-deal Brexit by seizing control of the parliamentary agenda from the government.
(Editing by Bernadette Baum and Will Dunham)
By Karen Brettell