The US military will deploy additional fighter jets and navy warships to the Middle East, the Pentagon said on Friday, as Washington braces for Iran and its regional allies to make good on a promise to respond to the killing of Hamas leader Ismail Haniyeh in Tehran.

After the back-to-back assassinations of Haniyeh in Tehran on Wednesday and top Hezbollah commander Fuad Shukr in Beirut the evening before, international diplomats have scrambled to head off a full-fledged regional war. Rising tensions have spurred a growing list of major airlines into cancelling flights to Tel Aviv or Beirut, including Lufthansa, Delta and Air India.

On Friday France urged its citizens to leave Iran and Cyprus said it had expanded plans to support a large-scale evacuation from the region if the war expands. The island nation helped tens of thousands of people leave during the 2006 war between Israel and Hezbollah.

The US defence secretary, Lloyd Austin, approved sending the additional Navy cruisers and destroyers – which can shoot down ballistic missiles – to the Middle East and Europe on Friday and the US will also send an additional squadron of fighter jets to the Middle East.