Iran warned Israel of escalation if it "does not end its aggression against the Palestinians". Iranian Foreign Minister Hossein Amirabdollahian said other parties in the region are ready to act, the semi-official Fars news agency reported on Sunday.
Iran's Supreme Leader Ayatollah Ali Khamenei said on Tuesday that Tehran was not involved in the Hamas militant group's attack on Israel, but hailed what he called the "irreparable" failure of Israel's military and intelligence.
Israel has long accused Iran's clerical rulers of fueling violence by supplying weapons to Hamas. Tehran says it provides moral and financial support to the group, which controls the Gaza Strip.
Supporting the Palestinian cause has been a pillar of the Islamic Republic since the 1979 revolution.
Foreign Minister Amiabdollahian, who last week accused Israel of committing "genocide" with its siege of the Gaza Strip, said an attack on Gaza would "open new fronts of resistance" in the Middle East.
"The responsibility for the possible opening of new resistance fronts in the region and any escalation of today's war falls squarely on the United States and the Zionist regime (Israel)," he said.
Amirabdollahian met with Hamas leader Ismail Haniyeh on Saturday in Qatar, where they discussed the group's deadly attack on Israel "and agreed to continue cooperation" to achieve the group's goals, Iran-backed Hamas said in a statement.
Earlier, Iranian President Ebrahim Raisi asked France to help "prevent oppression" of Palestinians in a phone call with his counterpart Emmanuel Macron.
President Macron's office said he warned his Iranian counterpart against any escalation of the conflict between Israel and Hamas.
"The president of the republic warned President Raisi against any escalation or expansion of the conflict, especially in Lebanon," Mr Macron's office said in a statement.
"Given its relations with Hezbollah and Hamas, Iran has a responsibility in this regard. Iran must do everything possible to avoid a regional explosion," he added.