Amir-Abdollahian also criticised the United States, which has given its unequivocal backing to Israel since the October 7 attacks by Hamas fighters that left 1,300 people dead in Israel.
Iran on Sunday warned that any Israeli ground offensive in the Gaza Strip could escalate conflicts elsewhere in the Middle East.
Foreign Minister Hossein Amir-Abdollahian held talks with Qatar's Emir Sheikh Tamim bin Hamad Al-Thani, as Israeli troops massed on the border.
"No one can guarantee the control of the situation and the non-expansion of the conflicts," he said, according to an Iranian foreign ministry statement.
"Those who are interested in preventing the scope of war and crisis from expanding, need to prevent the current barbaric attacks... against citizens and civilians in Gaza," he added.
Amir-Abdollahian also criticised the United States, which has given its unequivocal backing to Israel since the October 7 attacks by Hamas fighters that left 1,300 people dead in Israel.
Israeli air strikes aimed at Hamas leaders behind the deadly attack have killed more than 2,300. On both sides, the toll was mostly civilians.
Iran's top diplomat was in Qatar on Sunday as part of a regional tour that also included stops in Iraq, Lebanon and Syria.
Israel has stationed troops and tanks on its UN-patrolled northern border with Lebanon and closed a four kilometre wide zone to civilians after deadly exchanges of cross-border fire with Iran-backed militant group Hezbollah.
Western countries who support Israel have warned against a regional spillover of the conflict.
The United States has deployed a second aircraft carrier to the region in an effort to "deter hostile actions against Israel", Secretary of Defense Lloyd Austin said.
Hamas took more than 100 hostages in last weekend's attack.
Sunday's Iranian foreign ministry statement said Amir-Abdollahian had met high-ranking Hamas officials in Beirut and Doha who described "the issue of civilian prisoners as a priority" and would "take the necessary measures".
But there was no further detail on what those would be.
Speaking on CBS, White House National Security Advisor Jake Sullivan cited the possibility of a new battle front on the Israel-Lebanon border and added: "We can't rule out that Iran would choose to get directly engaged some way. We have to prepare for every possible contingency."
Iran is a long-time backer of the militant group Hamas and of Hezbollah in Lebanon, providing them funding and weapons.
"That is a risk and that's a risk that we have been mindful of since the start," Sullivan said of the prospect of Iran getting involved in the war, which was triggered by the Hamas attack on southern Israel from Gaza last weekend.
"It's why the president moves so rapidly and decisively to get an aircraft carrier into the eastern Mediterranean, to get aircraft into the Gulf, because he sent a very clear message to any state or any actor that would seek to exploit this situation," Sullivan added.
Defense Secretary Lloyd Austin announced the deployment of the second aircraft carrier on Saturday "to deter hostile actions against Israel or any efforts toward widening this war following Hamas's attack."
In the eastern Mediterranean the carrier USS Eisenhower and its accompanying ships will join the USS Gerald R. Ford, which was dispatched after the Hamas attack on October 7.