Iran has vowed revenge for the April 1 airstrike on its embassy compound in Damascus that killed a top Iranian general and six other Iranian military officers, escalating tensions in a region already shaken by the Gaza war.

"Right now it's very important for everyone to maintain restraint so as not to lead to a complete destabilisation of the situation in the region, which doesn't exactly shine with stability and predictability," Kremlin spokesperson Dmitry Peskov told at a news briefing.

"We call on all countries in the region to exercise restraint."

Conflict has spread across the Middle East since the eruption of the Gaza war, with Iran-backed groups declaring support for the Palestinians waging attacks from Lebanon, Yemen and Iraq. Tehran has avoided direct confrontation with Israel or the United States, while declaring support for its allies.

Israel has not claimed responsibility for the April 1 attack, for which Iranian Supreme Leader Ayatollah Ali Khamenei said on Wednesday Israel "must be punished and it shall be", adding that it was tantamount to an attack on Iranian soil.

BIDEN SAYS IRAN THREATENS 'SIGNIFICANT ATTACK IN ISRAEL'

U.S. President Joe Biden said on Wednesday Iran was threatening to launch a "significant attack in Israel", and that he had told Israeli Prime Minister Benjamin Netanyahu that "our commitment to Israel security against these threats from Iran and its proxies is iron-clad".

Iran is the third-largest oil producer in the OPEC group and oil prices rose after jumping a dollar a barrel in the previous session.

Late on Wednesday, an Iranian news agency published an Arabic report on the X platform saying the air space over Tehran had been closed for military drills, but then removed the report and denied it had issued such news.

In an apparent response to Khamenei, Israeli Foreign Minister Israel Katz said on Wednesday that Israel would respond if Iran attacked Israel from its own soil.

Russia's foreign ministry told citizens they should not travel to the Middle East, especially to Israel, Lebanon and the Palestinian territories.

Lufthansa said on Wednesday it had stopped flights to Tehran and on Thursday extended the suspension until probably April 13.

Lufthansa and its subsidiary Austrian Airlines are the only two Western carriers flying into Tehran, which is mostly served by Turkish and Middle Eastern airlines.

Austrian Airlines, which is owned by Lufthansa and flies from Vienna to Tehran six times a week, said it was still planning to fly on Thursday but was adjusting timings to avoid crew having to disembark for an overnight layover.

There was no immediate word from other international airlines. Iranian air space is also a key overflight route for Emirates' and Qatar Airways' flights to North America.

(Reporting by Ilona Wissenbach in Frankfurt, Shariq Khan in New York, Emily Chow in Singapore; Writing by Tom Perry and Ros Russell; Editing by Kevin Liffey)