Nouhad Mahmoud, the Lebanese special envoy, said: "It's unacceptable because people are still under shelling, bombardment and destruction is going on ... and people are dying."
Qatar, the only Arab nation on the council, received widespread support during closed council consultations for a press statement calling for an immediate ceasefire, restraint in the use of force, and the protection of civilians caught in the conflict, council diplomats said.
But Cesar Mayoral, Argentina's UN ambassador, said the United States objected to any statement and Britain opposed calling for a ceasefire.
The US and Britain want to wait for the outcome of this weekend's Group of Eight meeting in Russia, an Arab League foreign ministers meeting, and a mission sent to the Middle East by Kofi Annan, Mayoral and other diplomats said.
Jean-Marc de La Sabliere, the French ambassador to the UN and the current council president, confirmed that "there was no agreement on a text tonight, but we will meet on Monday".
But Mahmoud protested, saying while innocent civilians are killed "here we are impotent in having ... some stand to address the situation".
"It sends very wrong signals not only to the Lebanese people but to all Arab people, to all small nations that we are left to the might of Israel and nobody is doing anything," he said.
"It sends very wrong signals not only to all Lebanese people but to all Arab people"
Nouhad Mahmoud, Lebanese special envoy to the UN
"We want a resolution. We want a ceasefire. We want very clear stand from the Security Council. But concession after concession arrived to the press release - and even the press release was not possible to issue."
Lebanon's pro-Western government came to power after the assassination of Rafik al-Hariri, the former prime minister, in February 2005. This led to Syria's withdrawal of its forces from its smaller neighbour, ending a 29-year occupation.
"We have many reasons to expect much more from the Security Council," said Mahmoud, an ambassador who was sent from Beirut.
And from the United States?
"They were always supportive in the last one-and-a-half years, but when it comes to Israel it seems things change," he said.