The dollar index against a basket of six major currencies was up 0.15 percent at 96.155, trimming some of the previous day's losses.
The index had shed 0.4 percent overnight, when it stooped to 95.948, its lowest since Feb. 5. after Federal Chair Jerome Powell said that the U.S. central bank would remain "patient" on further interest rate hikes.
The euro slipped 0.1 percent to $1.1377 against the dollar, which tends to attract bids in times of political tensions and market turmoil due to its high liquidity.
The yen, another perceived safe haven, advanced to 110.38 per dollar from the previous day's close of 110.585 and also rose against the euro.
Pakistan downed two Indian jets on Wednesday, a day after Indian warplanes struck inside Pakistan for the first time since a war in 1971, prompting leading powers to urge the nuclear- armed rivals to show restraint.
"So far market reaction in major currencies has been relatively limited as tensions between the two countries had already been high. Focus is on whether the conflict shows signs of escalating," said Kyosuke Suzuki, director at Societe Generale in Tokyo.
The Indian rupee was down 0.4 percent at 71.36 per dollar as tensions gripped the subcontinent.
The Australian dollar, sensitive to shifts in risk sentiment, was a shade lower at $0.7182, and headed toward snapping a three-day winning run.
The pound was little changed at $1.3249 after surging more than 1 percent overnight to a five-month peak of $1.3288.
Sterling had rallied on Tuesday after British Prime Minister Theresa May offered lawmakers the chance to vote on delaying Brexit, opening up the possibility of avoiding a chaotic no-deal departure from the European Union.