Countries including India, France, Poland and Russia have warned their citizens against travel to the region, already on edge over the war in Gaza, now in its seventh month. White House National Security Council spokesman John Kirby said the threat from Iran was real and viable.
The Israeli military said it had not issued fresh instructions to civilians, but asked people to remain vigilant.
"Over the past day, the military has conducted a situational assessment and approved plans for a range of scenarios following reports and statements on an Iranian attack," chief military spokesman Daniel Hagari said in a televised statement on Friday.
Israel's foreign ministry did not comment on reports that some Israeli diplomatic missions had been partially evacuated and security stepped up.
"The revenge will come," wrote Israel's largest daily newspaper, Yedioth Ahronoth. "For the moment, the premise is that it will be very soon, in the next few days."
US President Joe Biden on Friday said he expected Iran to attack Israel "sooner, rather than later" and warned Tehran not to proceed.
Asked by reporters about his message to Iran, Biden said simply, "Don't," and he underscored Washington's commitment to defend Israel.
"We are devoted to the defense of Israel. We will support Israel. We will help defend Israel and Iran will not succeed," he told reporters at the White House after a virtual speech to a civil rights conference.
Israel did not claim responsibility for the air strike on April 1 that killed Brigadier General Mohammad Reza Zahedi, a senior commander in the Iranian Revolutionary Guard Corps' overseas Quds Force, and six other officers as they attended a meeting in the Damascus embassy compound.
But Iran's supreme leader, Ayatollah Ali Khamenei, said Israel "must be punished and shall be" for an operation he said was equivalent to an attack on Iranian soil.
"It's going to be very difficult for Iran not to retaliate," said Raz Zimmt, senior researcher at Israel's Institute for National Security Studies.
"I still believe that Iran doesn't want to engage in full-scale, direct military confrontation against Israel, and certainly not with the United States. But it has to do something."
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