Markets are also bracing for a week packed with central bank meetings.
As both Iran and Israel showed no signs of backing off from their attacks, market participants mulled the prospect that Tehran might seek to choke off the Strait of Hormuz, the world's most important gateway for oil shipping, which could raise broader economic risks from disruptions in the energy-rich Middle East.
Crude prices were up about 1% after closing 7% higher on Friday following Israel's preemptive strike on Iran.
On Monday, the dollar was flat at 144.08 Japanese yen after rising nearly 0.4% earlier in the session, while the euro was muted at $1.1555.
The greenback was also steady against the Swiss franc at 0.811, while an index that measures the dollar against six other currencies dipped 0.1% and was last at 98.11.
Currencies that are positively correlated to risk such as the Australian dollar and the New Zealand dollar were marginally higher, while oil exporter Norway's krone firmed 0.3% to hit its highest since early 2023.
"The Dollar's role as a safe haven will surely be tested, and recent price action has been inconclusive," said Win Thin, Global Head of Markets Strategy at Brown Brothers Harriman.
"If the Fed delivers a dovish hold as we expect, the dollar is likely to resume weakening due to the worsening fundamental backdrop in the US," Thin said.
--Reuters--