Israeli army spokesman Jonathan Conricus warned that Hezbollah was playing “a very, very dangerous game”.
Iran’s Foreign Minister Hossein Amir-Abdollahian has warned Israel that the Middle East could spiral out of control if it does not stop strikes on Gaza.
He said the US was also “to blame” for providing military support to Israel.
Hours later, Israeli PM Benjamin Netanyahu warned troops his people were in a battle for their lives and said the war against Hamas was “do or die”.
Iran supports both Hamas, which attacked Israel two weeks ago killing 1,400 people, and Lebanon’s Hezbollah.
More than 4,600 Palestinians have been killed in the last two weeks in Gaza, according to the Hamas-run health ministry, and Israel announced on Saturday that it was intensifying air strikes.
“I warn the US and its proxy Israel that if they do not immediately stop the crime against humanity and genocide in Gaza, anything is possible at any moment and the region will go out of control,” Mr Amir-Abdollahian said at a news conference in Tehran.
He said that the results could be “severe, bitter” and “have far-reaching repercussions”, both regionally and for those advocating for war.
The foreign minister added that US military support for Israel was evidence that the ongoing conflict in Gaza was “a proxy war carried out by Israel on behalf of the United States”.
Top US officials are also warning the conflict could spread.
US Defence Secretary Lloyd Austin warned of the prospect of “significant escalation of attacks” on US troops or citizens.
“If any group or any country is looking to widen this conflict and take advantage of this very unfortunate situation… our advice is: don’t,” he said on the ABC network’s This Week programme.
US Secretary of State Antony Blinken also mentioned a “likelihood of escalation” from Iranian proxies, such as Hezbollah or Hamas, and said the US was “taking every measure to make sure we can defend” Israelis and US citizens.
Several Iraqi bases used by US-led coalition troops have been targeted in drone and rocket attacks in recent days.
Also on Sunday, Mr Netanyahu paid a visit to troops in northern Israel near the border with Lebanon, which has seen exchanges of fire with Hezbollah since the early days of the conflict.
“We’re in a battle for our lives. A battle for our home, this is not an exaggeration, this is the war. It’s do or die – they need to die,” he said.
He warned Hezbollah not to enter the war.
“[Hezbollah] will be making the biggest mistake of their lives. And we will hit them with an unimaginable force. It will mean devastation for them and the state of Lebanon,” he said.
For its part, Hezbollah has declared that it is “fully ready to fight against Israel”.
At least 27 people have been reported killed in southern Lebanon during exchanges of fire between Israel and Hamas. At least five Israeli soldiers and one civilian have been killed in Israel, according to Israeli military reports.
Israel has ordered dozens of northern communities to evacuate, adding 14 more on Sunday.
And in neighbouring Syria – where Iran has a military presence – Israeli missiles hit Damascus and Aleppo international airports early on Sunday, killing at least two workers, according to Syrian state media.
Both airports have been taken out of use given the damage to their runways.
