Nouhad Mahmoud, a Lebanese foreign ministry official, made his plea at an emergency session of the 15-nation council.
But members said they planned no immediate action apart from a statement welcoming a decision by Kofi Annan, the UN secretary-general, to send a team to the region to encourage restraint.
The United States vetoed a resolution on Thursday drafted by Arab nations calling on Israel to end a separate two-week military incursion in Gaza.
John Bolton, the US ambassador, called the measure "not only untimely, but already outmoded" and biased against Israel.
Mahmoud said Israel's actions against his country were "aimed at bringing Lebanon to its knees and subverting it by any means".
"I do not need to explain to you here who the victim is and who the aggressor is," he said.
He asked the council "to take an immediate and clear decision calling for a comprehensive, immediate ceasefire, a lifting of the air and sea blockade imposed upon Lebanon and calling for an end to Israeli aggression".
However, Dan Gillerman, the Israeli ambassador to the UN, said the Lebanese government had brought trouble on itself by allowing the resistance movement Hezbollah to remain armed.
He said this gave it de facto control over southern Lebanon and enabled it to cross the border to seize two Israeli soldiers.
'Axis of terror'
"Lebanon is today occupied by terror," he said, accusing Hezbollah of comprising "an axis of terror" along with Hamas, the governing Palestinian group, and Syria and Iran, which he said supported Hamas and Hezbollah.
He urged Lebanon to extend its authority across all of its territory "and exercise sovereignty over a free Lebanon".
Ibrahim Gambari, the UN undersecretary-general for political affairs, said that escalation was "in no one's interest".
"The space for diplomatic initiative is quickly closing," he said.