France requested the urgent talks in the 15-member council after two Israeli soldiers and a Spanish UN peacekeeper died in the exchange of fire between Israeli forces and Hezbollah fighters.
The violence raised fears of another all-out conflict between the two countries, who fought a month-long war in 2006, in a region already wracked by fighting with Islamist fighters in Syria and Iraq.
Tension in the area has been building, especially after an Israeli air strike on the Syrian sector of the Golan Heights killed six Hezbollah fighters and an Iranian general on January 18.
"Israel will not stand by as Hezbollah targets Israelis," wrote Ron Prosor in the letter also sent to Secretary General Ban Ki-moon.
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The Israeli envoy demanded that the council condemn Hezbollah and take steps to press Lebanon to disarm the Islamist militants as outlined in UN resolutions.
The clashes began when Hezbollah fired an anti-tank missile at a military convoy in the Israel-occupied border area, prompting Israel to respond with air and ground strikes.
The 10,000-strong UNIFIL mission said it had observed six rockets fired towards Israel from southern Lebanon and that Israeli forces "returned artillery fire in the same general area".
The council will be meeting behind closed doors and hear a report from a senior peacekeeping official overseeing UNIFIL operations.
Israel occupied parts of Lebanon for 22 years until 2000 and the two countries are still technically at war.
In 2006, Israel fought a bloody war against Hezbollah that killed more than 1,200 people in Lebanon, mostly civilians, and some 160 Israelis, mostly soldiers.