The franc rose 0.2% to 0.7674 per dollar and rose 0.6% to its strongest level since 2015 at 0.9030 against the euro in the early hours of the Asian session.
The euro fell 0.3% to $1.1781 and the yen rose early but was held back by big oil imports from Japan, and last traded slightly weaker at 156.32 against the dollar.
Sterling and the Australian dollar fell more than 0.5% and the Chinese yuan fell about 0.2% in offshore trade, as China is an energy importer and a major buyer of Iranian oil.
“You don’t know how long this is going to last, how long the oil high is going to last, how long the Strait of Hormuz is going to be closed,” said Jason Wong, a BNZ strategist in Wellington.
“The first reaction is low risk, and you have to take each day as it comes.”
Israel’s military said its air force had killed Khamenei, and his death at the age of 86 was confirmed by Iranian state media, setting off a high-profile succession race. The attacks extended on Sunday and Iran responded, with Iran’s Revolutionary Guards saying they had targeted three US and British oil tankers, while explosions were reported in Dubai and Doha.
Oil prices are the primary focus of the markets and are up around 9% in early Monday trading on mixed trading.
The currencies of exporters such as Canada and Norway were stable in the Asian morning.
The risk-sensitive Australian dollar fell 0.7% to $0.7065, although traders thought more sustained pressure was likely to come from energy importers.
“The euro is in a difficult spot,” Wells Fargo analysts said in a note.
“The European natural gas storage season is about to begin and the EU is moving forward with record low gas in storage, which means it will need to buy a larger share of energy as prices are likely to be higher.”
The spokesman of the Israeli army, Lt. Col. Nadef Shoshani, said that many targets remain, but the deployment of ground forces has not been considered. US President Donald Trump told the Daily Mail that the campaign could last a month.
“We thought it would be four weeks. It’s always a four-week process,” he said.
Shipping data on Sunday showed that at least 150 tankers, including crude oil and liquefied natural gas vessels, were anchored in the open waters of the Gulf beyond the Strait of Hormuz, and dozens more were docked on the other side of the Strait.
