Although Tehran has been a long-term backer of Hamas, Iranian officials have been adamant that the country had no involvement in the militants' attack against its arch enemy Israel on Saturday.

Nevertheless, the United States fears the opening of a second front on Israel's northern border with Lebanon if Hezbollah, another heavily armed Islamist group backed by Iran, were to intervene.

"Officials of some countries contact us and ask about the possibility of a new front (against Israel) being opened in the region," said Foreign Minister Hossein Amir-Abdollahian during a meeting with Iraqi Prime Minister Mohammed Shia al-Sudani.

"We tell them that our clear answer regarding future possibilities is that everything depends on the actions of the Zionist regime in Gaza," he said, according to a statement from the Iranian foreign ministry.

"Even now, Israel's crimes continue and no one in the region asks us for permission to open new fronts."

Later on Thursday, Abdollahian arrived in the Lebanese capital Beirut, where he was received by Hezbollah and Hamas among other pro-Iran groups.

He is scheduled to meet Lebanese officials on Friday before heading to Damascus.

Speaking from Beirut's airport, the top diplomat said that Iran's regional allies, known as the "axis of resistance", could respond if Israel's Gaza offensive escalates.

"The continuation of war crimes against Palestinians and Gaza will receive a response from the rest of the axes," he told reporters.

At least 1,200 Israelis, foreigners and dual citizens were killed by Hamas militants during its attack on Saturday.

In Gaza, health officials reported 1,417 Palestinians killed by Israel's retaliatory barrages against the coastal enclave.

The West has been cautious about Iran since Saturday, but its leaders have warned Tehran in no uncertain terms against intervening in the war.

US President Joe Biden said on Wednesday that he had "made it clear to the Iranians: Be careful".

After Iraq, Amir-Abdollahian will travel to Lebanon, where Hezbollah has, so far, been content to hold back from joining the war triggered by its ally Hamas.

In a call with his Syrian counterpart Bashar al-Assad, Iranian President Ebrahim Raisi on Wednesday appealed to "all the Islamic and Arab countries" to "reach serious convergence and cooperation on the path of stopping the crimes of the Zionist regime against the oppressed Palestinian nation".