- Iran has vowed to retaliate after Israel struck the Iranian consulate in Syria 11 days ago, killing 13 people.
- UK Foreign Secretary Lord Cameron has phoned his Iranian counterpart to urge against further escalation.
The United States has restricted travel for its employees in Israel amid fears of an attack by Iran.
The US embassy said staff had been told not to travel outside the greater Jerusalem, Tel Aviv or Be'er Sheva areas "out of an abundance of caution".
Iran has vowed to retaliate after Israel struck the Iranian consulate in Syria 11 days ago, killing 13 people.
UK Foreign Secretary Lord Cameron has phoned his Iranian counterpart to urge against further escalation.
Israel has not claimed responsibility for the consulate attack but is widely considered to have been behind it.
Iran backs Hamas, the Palestinian group fighting Israel in Gaza, as well as various proxy groups throughout the region, including some - such as Hezbollah in Lebanon - that frequently carry out strikes against the Israelis.
Those killed in the consulate attack included a senior commander of Iran's elite Quds Force in Syria and Lebanon, as well as other military figures.
The attack came at a time of continuing diplomatic efforts to prevent the war in Gaza spreading across the region.
Speaking on Wednesday, US President Joe Biden warned Iran was threatening to launch a "significant attack" and vowed to offer "ironclad" support to Israel.
The commander responsible for US operations in the Middle East, Erik Kurilla, has travelled to Israel for talks with officials on security threats.
The Pentagon said the visit had been scheduled previously but had been brought forward "due to recent developments."
Following a call with Iranian Foreign Minister Hossein Amir-Abdollahian, Lord Cameron said he had "made clear... that Iran must not draw the Middle East into a wider conflict".
"I am deeply concerned about the potential for miscalculation leading to further violence," he said.
US Secretary of State Antony Blinken has spoken to the foreign ministers of China, Saudi Arabia, and Turkey to argue that further escalation is not in anyone's interest.
It is not clear what form any reprisal attack would take nor whether it would come directly from Iran or via one of its proxies.
On Sunday an Iranian official warned Israel's embassies were "no longer safe", suggesting a consulate building could be a possible target.
Israeli Defence Minister Yoav Gallant has told his US counterpart that "any direct Iranian attack" on Israeli territory would "require an appropriate Israeli response against Iran".
Asked about the travel restrictions on Thursday, state department spokesperson Matthew Miller said he would not disclose the "specific assessments" behind them, but added: "Clearly we are monitoring the threat environment in the Middle East and specifically in Israel."
The UK Foreign Office has also updated its travel advice for Israel to state that the country's government has raised the "possibility of an attack on Israeli territory from Iran, and that such an attack could trigger wider escalation".
Since the Hamas-led attack on Israel on 7 October, the Foreign Office has warned against travel to large parts of Israel and the Occupied Palestinian Territories.
German airline Lufthansa has extended a suspension of flights to the Iranian capital Tehran until Saturday.
The October attack saw gunmen kill 1,200 people and take more than 250 hostage after crossing into Israel from Gaza.
Israel says that of 130 hostages still in Gaza, at least 34 are dead.
More than 33,000 Gazans, the majority of them civilians, have been killed during Israel's subsequent offensive in Gaza, the Hamas-run health ministry says.