Israel was widely blamed for an April 1 attack that destroyed Iran's consulate building in Damascus and killed seven Revolutionary Guards, including two generals.
Iran's supreme leader, Ayatollah Ali Khamenei, warned Wednesday that Israel "must be punished and will be punished", days after one of his advisers said Israeli embassies are "no longer safe."
Israeli Foreign Minister Israel Katz swiftly replied on social media site X that "if Iran attacks from its territory, Israel will respond and attack Iran."
Biden said he had told Israeli Prime Minister Benjamin Netanyahu that "our commitment to Israel's security against these threats from Iran and its proxies is ironclad."
US Central Command chief Michael Kurilla was in Israel on Thursday to discuss the situation with Defence Minister Yoav Gallant, the Pentagon said.
"We warned Iran," White House Press Secretary Karine Jean-Pierre told a briefing without elaborating.
The US embassy in Israel also announced it was restricting the movements of its diplomats over security fears, saying that "out of an abundance of caution" staffers and their family could not undertake personal travel outside the Tel Aviv, Jerusalem and Beersheeva areas "until further notice."
During a visit to an airbase in central Israel, Netanyahu spoke of "challenging times" on multiple fronts.
"We are in the middle of the war in Gaza which continues in full force... but we are also preparing for scenarios of challenges from other arenas," he said in comments released by his office.
Moscow called on both Iran and Israel to exercise restraint.
German Foreign Minister Annalena Baerbock urged "maximum restraint", and Lufthansa said it had extended a temporary suspension of Iran flights until Saturday.
Iranian Foreign Minister Hossein Amir-Abdollahian said he had received phone calls Thursday from Baerbock as well as her British and Australian counterparts.
In a post on X, he said he had told them that "when the Zionist regime breaches the immunity of diplomatic persons and places" and the UN Security Council fails to condemn it, "legitimate defence... is a necessity."
Israel and the United States have long faced off against Iran and its so-called "Axis of Resistance" allies based in Lebanon, Iraq, Syria and Yemen.
Regional tensions have been stoked by the Gaza war which began after Hamas's unprecedented October 7 attack against Israel left 1,170 people dead, mostly civilians, according to Israeli figures.
Palestinian fighters also took about 250 hostages, 129 of whom remain in Gaza, including 34 the Israeli army says are dead.
Iran has said it had no advance knowledge of October's attack but has hailed the assault.
Israel's retaliatory offensive has killed at least 33,545 people in Gaza, mostly women and children, according to the Hamas-run territory's health ministry.
Hamas said 20 people were killed in Israeli bombardments on Thursday. It said two schools and two mosques were among the buildings hit and an imam was among the dead.
In the Nuseirat area, which took the brunt of the bombing, Imad Abu Shawish, 39, said "the situation is dire and still getting worse. Bombardment hasn't stopped and is still happening now."
Much of Gaza has been reduced to a bomb-cratered wasteland, with yet more bodies feared under the rubble.
An Israeli siege has deprived Gaza's 2.4 million people of most food, water, fuel and medicines, the dire shortages only alleviated by sporadic aid deliveries.
Israeli war cabinet member Benny Gantz said Wednesday "Hamas is defeated" militarily but pledged to keep fighting "what remains of it" in the years to come.
An Israeli air strike on Wednesday killed three sons of Hamas's Qatar-based leader Ismail Haniyeh.
Haniyeh insisted their deaths would not influence Hamas's position in ongoing talks in Cairo for a truce and hostage release deal.
Those talks, which started Sunday, have brought no breakthrough on a plan presented by US, Qatari and Egyptian mediators, which Hamas said it was studying.
The framework plan would halt fighting for six weeks and see the exchange of about 40 hostages for hundreds of Palestinian prisoners, as well as more aid deliveries.
Biden said that "it's now up to Hamas, they need to move on the proposal that's been made."
Israel accused Hamas Thursday of "walking away" from what government spokesman David Mencer called "a very reasonable offer on the table."
Hamas official Bassem Naim said only a ceasefire could provide "enough time and safety" to locate Israeli hostages held across the territory and ascertain their fate because they are held by different groups.
Washington has ramped up pressure on Netanyahu to agree to a truce, increase aid flows and abandon plans to send troops into Gaza's far-southern city of Rafah where about 1.5 million civilians are sheltering.
Rafah is the last Gazan city yet to face a ground incursion.
Gallant promised Israel would "flood Gaza with aid", using an Israeli crossing point, streamlined checks and two new routes organised with Jordan.
He said they expected to reach 500 aid trucks a day, the pre-war average.
However, a UN Security Council statement Thursday said "more should be done to bring the required relief given the scale of needs in Gaza."
Israel has faced a chorus of international criticism over its handling of the war.
Spain is among several Western nations, including Ireland and Australia, to have suggested they would recognise a Palestinian state as a starting point for wider peace talks.
Spanish Prime Minister Pedro Sanchez warned that Israel's "disproportionate response" in Gaza risked "destabilising the Middle East and, as a consequence, the entire world."
