Iran warned Israel that any new military "adventures" in Lebanon could lead to "unforeseen consequences".
UN Secretary-General Antonio Guterres condemned Saturday's rocket fire and called on all parties to "exercise maximum restraint".
Israel's army called it "the deadliest attack on Israeli civilians" since the October 7 attack that began the current fighting in Gaza and triggered regular exchanges of fire across the Lebanese border.
Israel blamed Lebanon's Hezbollah movement for firing a Falaq-1 Iranian rocket but the group, said it had "no connection" to the incident.
It said, however, that it had fired one such rocket on Saturday towards an Israeli military target in the Golan.
The rocket fire in Majdal Shams, whose population are Arabic-speaking Druze, prompted Israeli Prime Minister Benjamin Netanyahu to return early from the United States.
Upon arrival he went immediately into a security cabinet meeting, his office said.
"Hezbollah will pay a heavy price" for the attack, "a price it has not paid before", he said.
After the meeting, his office said: "The members of the cabinet authorised the prime minister and the defence minister to decide on the manner and timing of the response against the Hezbollah terrorist organisation." It offered no further details.
Defence Minister Yoav Gallant earlier Sunday visited the scene of the attack and vowed Israel would "hit the enemy hard".
Israel's foreign ministry said Hezbollah had "crossed all red lines".
In expectation of Israel's retaliation, Hezbollah evacuated several positions close to the border and in eastern Lebanon, a source close to the group said.
Israel's military said later Sunday it had hit Hezbollah targets "both deep inside Lebanese territory and in southern Lebanon".
An Israeli drone fired two missiles at Taraiyya village in eastern Lebanon, destroying a hangar and a home without causing casualties, a Lebanese security source told AFP.
Hezbollah has said its cross-border fire is an act of support for Hamas who have been fighting Israel's military in Gaza since October 7, when they attacked southern Israel.
That attack resulted in the deaths of 1,197 people in Israel, mostly civilians, according to an AFP tally based on official Israeli figures.
Militants also seized 251 hostages, 111 of whom are still held captive in Gaza, including 39 the military says are dead.
Israel's retaliatory military campaign in Gaza has killed at least 39,324 people, according to the health ministry in the Hamas-run territory, which does not provide details on civilian and militant deaths.
In Gaza's southern city of Khan Yunis on Sunday, the civil defence agency reported five killed in an Israeli strike that hit several tents housing displaced Palestinians in a humanitarian zone.
Israel's military ordered the evacuation of several blocks of Al-Bureij and Al-Shuhada in central Gaza, warning that it would "operate forcefully" there.
Separately, Philippe Lazzarini, who heads the UN agency for Palestinian refugees, said on social media site X that only "14 percent of areas in Gaza" were not subject to evacuation orders.
He accused Israel of creating "havoc and panic" with frequent evacuation orders.
The rocket strike on Majdal Shams hit a football pitch and killed children who local authorities said were aged 10 to 16. An 11-year-old boy earlier reported missing after the attack was in fact the 12th fatality, police confirmed late Sunday, Israeli media said.
Thousands of residents crowded the town's streets in a tearful funeral ceremony for many of the dead.
Riad Kahwaji, head of the Institute for Near East and Gulf Military Analysis, said the position Hezbollah said it targeted is about 2.4 kilometres (1.5 miles) from the town, putting it "within margin of error" of the inaccurate rockets.
But "the possibility of a misfire" from an Israeli air-defence missile could not be ruled out and there should be an independent investigation, he added.
The rocket fire on Majdal Shams came after an Israeli strike killed four Hezbollah fighters in south Lebanon, prompting the militant group to launch retaliatory rocket attacks against the Golan and northern Israel.
The White House said the rocket launch was "conducted by Lebanese Hezbollah", adding that "it was their rocket and launched from an area they control".
The UN special coordinator for Lebanon, Jeanine Hennis-Plasschaert, and UN Interim Force in Lebanon (UNIFIL) chief Aroldo Lazaro said in a joint statement that intensifying exchanges of fire "could ignite a wider conflagration that would engulf the entire region in a catastrophe beyond belief".
Lebanon urged "an immediate cessation of hostilities on all fronts", later calling for an "international investigation" into the strike.
Iran's foreign ministry spokesman Nasser Kanani warned that "any ignorant action of the Zionist regime can lead to the broadening of the scope of instability, insecurity and war in the region".
Israel's foreign ministry called the incident in Majdal Shams a "massacre", accusing Hezbollah of deliberately targeting civilians.
Many residents of the Druze town have not accepted Israeli nationality since Israel seized the Golan Heights from Syria in 1967.
Syria denounced Israel's "false accusations" against Hezbollah and said Israel was looking for "pretexts to enlarge its aggression".
Cross-border fire since October has killed at least 527 people in Lebanon, according to an AFP tally. Most of the dead have been fighters but the toll includes at least 104 civilians.
According to Israel's army, 22 soldiers and 24 civilians have been killed so far in northern Israel.
Hezbollah chief Hassan Nasrallah has said that if a ceasefire was reached in Gaza, his movement would stop cross-border attacks.
Blinken said the best way to prevent the Gaza conflict from escalating "is to get the ceasefire in Gaza that we're working so hard on".
Months of effort have failed to secure a deal, but Egyptian state-linked media said talks were to take place Sunday in Rome.
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