The WSJ Dollar Index, which measures the dollar against 16 other currencies, rose 0.2% to 87.23.
The dollar has benefited from demand for assets seen as safe in the wake of the June 23 U.K. vote to leave the European Union. But analysts say the greenback's rise will be put to the test this week by new economic data and reports.
A stronger-than-expected reading of the The Institute for Supply Management's June nonmanufacturing index Wednesday helped ease concerns about a slowdown in the sector.
Investors are also looking to the release of minutes from the Fed's June 14-15 policy meeting at 2 p.m. EDT for more insight into officials' concerns about a slowdown in the broader economy and about the impacts of the Brexit vote. The Fed kept rates unchanged at the June meeting, and markets are now pricing in little chances of an interest-rate increase this year.
Friday's June U.S. jobs report will also offer a snapshot on the health of the labor market after a disappointing May reading.