But the Israeli-Lebanese border was calm, as officials in the Jewish state played down the threat of a new war with Lebanon's Iran-backed Shiite militant group.
In a rare such declaration, Defence Minister Moshe Yaalon said Hezbollah had passed on a message through the United Nations peacekeeping mission in south Lebanon, UNIFIL, saying it did not want a further escalation.
"We have received a message... That, from their point of view, the incident is over," he told public radio.
The two soldiers were killed yesterday when Hezbollah fired anti-tank missiles at a convoy in an Israeli-occupied area on the border with Lebanon.
Israeli forces responded to the attack -- which came in retaliation for an Israeli strike on the Golan Heights that killed senior Hezbollah members -- with artillery, tank and air fire on several villages in southern Lebanon.
There were no reports of Lebanese casualties, but a 36-year-old Spanish peacekeeper with UNIFIL was killed in the exchange of fire.
In the Lebanese border village of Majidiya, residents collected spent artillery shells from yesterday's strikes, an AFP photographer said.
At the local UN base a blackened concrete tower could be seen with part of its wall blown out, and a Spanish flag flew at half-mast.
Hundreds of mourners gathered at Mount Herzl military cemetery in Jerusalem for the burial of 25-year-old Captain Yochai Kalangel.
Sobbing relatives greeted mourners, many wearing the purple beret of Kalangel's Givati (Highland) Brigade.
There was a similar turnout for the other soldier killed, 20-year-old Staff Sergeant Dor Chaim Nini, buried in the town of Shtulim in south-central Israel.
Israel said it considered yesterday's attack the "most severe" since 2006, when war with Hezbollah killed more than 1,200 people in Lebanon, mostly civilians, and some 160 Israelis, most of them soldiers.
Prime Minister Benjamin Netanyahu blamed the attack on Iran.
"This is the same Iran that is now trying to achieve an agreement, via the major powers, that would leave it with the ability to develop nuclear weapons," he said.
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