The US embassy in Baghdad has called on its citizens to leave Iraq in the wake of the assassination of Iran’s top general, as Washington and its regional allies scrambled to protect themselves against a possible military response.

“Due to heightened tensions in Iraq and the region, the US embassy urges American citizens to … depart Iraq immediately,” the embassy said in a statement. “US citizens should depart via airline while possible, and failing that, to other countries via land.”

Several other US diplomatic missions warned citizens to be aware of their surroundings, and the US embassy in Kuwait said it had increased its security, although it said it was not aware of specific threats. Israel and Saudi Arabia, both US allies who consider Iran their arch-enemy, also braced for potential retaliatory strikes.

Without providing details, Iran has promised “severe revenge” for the killing of Qassem Suleimani. Its regional partners, the Lebanon-based Hezbollah group and Iraqi militias have also said the death will be avenged.

It is widely feared that the pre-dawn attack, ordered by Donald Trump, could become a critical turning point in an escalating conflict between Washington and Tehran. As well as embassies and consulates across the Middle East, the US has multiple army bases, including in Kuwait, Turkey and Iraq.

Other countries have also taken measures following the attack. Germany’s defence ministry said it had ordered its soldiers in Iraq not to leave their bases. Germany has roughly 130 soldiers deployed to the country who are tasked with training Iraqi security forces.

Israel, which has fought an increasingly overt war with Iranian forces in neighbouring Syria, took defensive steps including closing a ski resort near the Syrian border and upping security measures at its embassies.

Benjamin Netanyahu was due to cut short a diplomatic visit to Greece and fly home early, his office said. In a short statement, Netanyahu – who has long been calling for more aggressive action against Iran – praised Trump for what he said was swift, forceful and decisive action. In Tel Aviv, Israel’s defence minister, Naftali Bennett, met the head of the army on Friday morning.

Speaking to the public broadcaster KAN, Ram Ben Barak, a former deputy director of Israel’s Mossad intelligence agency, said the country should “prepare for the eventuality that Iran will decide to make a mistake and respond in our direction, even though we are not involved. That means increased intelligence listening, that means being prepared to intercept, that means operational ability if intelligence says that is necessary.”

China, Russia and France all criticised the US attack. “We are waking up in a more dangerous world. Military escalation is always dangerous,” France’s deputy minister for foreign affairs, Amelie de Montchalin, told RTL radio. “When such actions, such operations, take place, we see that escalation is under way.”

Tensions between Iran and the US have been escalating for months. Washington has imposed tightening sanctions while Tehran has restarted nuclear activity and entrenched its military in neighbouring countries.

In some of the most explosive developments, the US blamed Iran for damaging oil tankers in the Gulf and for aerial attacks on Saudi oil facilities. Tehran has denied involvement.