The United States has increased economic and military pressure on Iran, with U.S. President Donald Trump on Thursday urging its leaders to talk to him about giving up their nuclear program and saying he could not rule out an armed confrontation.
Prime Minister Benjamin Netanyahu's government, which supports Trump's hard tack against its arch-foe, has largely been reticent about the spiralling tensions.
But Steinitz told Ynet on Sunday that "things are heating up" in the Gulf.
"If there's some sort of conflagration between Iran and the United States, between Iran and its neighbours, I'm not ruling out that they will activate Hezbollah (in Lebanon) and Islamic Jihad from Gaza, or even that they will try to fire missiles from Iran at the State of Israel," said Steinitz, a member of Netanyahu's security cabinet.
Hezbollah and Islamic Jihad are Iranian-sponsored guerrilla groups on Israel's borders.
The IDF declined to comment when asked if it was making any preparations for possible threats linked to the Iran-U.S. standoff.
Israel has traded blows with Iranian forces in Syria, as well as with Hezbollah in Lebanon and Palestinian militants. But it has not fought an open war with Iran, a country on the other side of the Middle East.
Meanwhile, the new commander of Iran's elite Revolutionary Guards Hossein Salami told Iranian parliamentarians on Sunday that the United States has started a psychological war in the region, according to a government spokesman.
The U.S. military has sent forces, including an aircraft carrier and B-52 bombers, to the Middle East to counter what the Trump administration says are "clear indications" of threats from Iran to U.S. forces there.
The USS Abraham Lincoln is replacing another carrier rotated out of the Gulf last month.
"Commander Salami, with attention to the situation in the region, presented an analysis that the Americans have started a psychological war because the comings and goings of their military is a normal matter," the spokesman for the parliamentary leadership, Behrouz Nemati, said, summarizing the Guards commander's comments, according to parliament's ICANA news site.
Major General Hossein Salami was appointed as head of the Guards last month.