The yen and other safe-haven currencies were in demand on Monday, along with assets such as gold, as investors fretted that the killing of Iran's most prominent military commander by the United States could trigger a broader Middle East conflict.
The moves extended a flight to safety that began on Friday after Iranian Major-General Qassem Soleimani was killed in a US drone strike on his convoy at Baghdad airport.
US President Donald Trump warned of a "major retaliation" if Iran hit back, while Iran's replacement commander vowed to expel the United States from the region.
On Sunday, Iran further distanced itself from the 2015 nuclear agreement with world powers, which the United States withdrew from in 2018, saying it would continue to cooperate with the UN nuclear watchdog but would respect no limits to its uranium enrichment work.
The Japanese yen surged on Monday to a three-month high of 107.77 versus the US dollar in Asian trading and was last up 0.2% on the day just below 108.
Spot gold was 1.6% higher, at an almost seven-year high, and oil rose on fears that any conflict in the region could disrupt global supplies.
The Swiss franc, another safe currency, was trading flat too, though close to the four-month high of 1.0824 it reached against the euro on Friday.
Implied volatility gauges in euro/dollar, the most traded currency pair, on the other hand, were relatively calm, suggesting investors are not yet fleeing to add protection to their portfolios by buying currency options.
A currency volatility index developed by Deutsche Bank was only marginally up and still close to its lowest levels on record.
Currencies sensitive to global risk appetite were weaker, including the Australian dollar, New Zealand dollar and Swedish crown.
"Iran is almost certainly to respond in some scale, scope and magnitude," said Lee Hardman, currency analyst at MUFG.
Therefore "market participants are likely to remain nervous until there is more clarity over how geopolitical tensions between the US and Iran will proceed," Hardman said, noting that geopolitical tensions could hurt global economic growth, especially if the price of oil increases.
So far, however, oil-related currencies such as the Canadian dollar, Norwegian crown and Russian rouble have not yet strengthened even though Brent crude continued last week's rise and topped $70 on Monday for the first time since September.
The dollar was 0.2% lower against six major currencies and down 0.4% against the euro at $1.1196.
Jane Foley, senior currency strategist at Rabobank, said the dollar might be losing out on the back of other safe-haven currencies rising.
The dollar is sometimes seen as a safe-haven asset given most central banks hold it as their main reserve currency and a big chunk of global companies trade using dollars, but the yen and the franc represent a more traditional safe-haven bet.
Foley expects the greenback to weaken during the course of 2020.
Elsewhere, the British pound was trading up 0.7% at $1.3160 and up 0.4% at 85.04 pence against the euro ahead of a crucial week when British lawmakers are due to reconvene to debate the EU divorce deal Prime Minister Boris Johnson has agreed with Brussels.