Israel says it would be "difficult if not inconceivable" to accept nations which do not recognise its right to exist as part of a UN force in Lebanon.
Mass burials are being held for victims of the conflict
Israeli UN envoy Dan Gillerman was speaking after Indonesia and Malaysia, which do not recognise Israel, pledged troops for the UN deployment.
Malaysia said Israel should have no say in the make-up of the force.
The UN has expressed cautious optimism that it can deploy an initial 3,500-strong force within two weeks.
UN deputy chief Mark Malloch Brown warned earlier that delay could threaten the ceasefire.
But building the force has proved problematic. Mr Malloch Brown said a lot of work was needed in the coming days to meet the two-week deadline.
There is concern that the offers do not necessarily provide the right mix of troops and capabilities needed for the deployment, the BBC's Bridget Kendall in New York says.
A number of countries are calling for clearer guidance on the exact nature of the mission.
UN TROOP PLEDGES
France - leadership and 200 troops
Bangladesh - two battalions (up to 2,000 troops)
Malaysia - one battalion (up to 1,000 troops)
Indonesia - one battalion, an engineering company
Nepal - one battalion
Denmark - at least two ships
Germany - maritime and border patrols
Sources: UN diplomats
France, which agreed to lead the force once its mandate had been set, said it would send only 200 extra troops immediately, far fewer than expected.
The UN had hoped for a larger European contingent and was disappointed by France's offer.
But French Defence Minister Michele Alliot-Marie defended the decision. "You can't send in men telling them: Look what's going on but you don't have the right to defend yourself or to shoot," she told RTL radio.
Italy's government has approved the deployment of troops, saying it would decide how many in the coming days. Officials said as many as 3,000 troops could be sent.
Bangladesh and Nepal have also pledged troops, while Germany has offered a maritime task force. The UK and the US say they will provide logistical support.
As the UN's efforts to build the force continued, Mr Gillerman made clear Israel's unhappiness with some of the contributors.
"It would be very difficult if not inconceivable for Israel to accept troops from countries who do not recognise Israel, who have no diplomatic relations with Israel," he told the BBC.
He said they would be "very happy" to accept troops from Muslim countries they have friendly relations with.
"But to expect countries who don't even recognise Israel to guard Israel's safety I think would be a bit naive," he said.
His comments were dismissed by Malaysia, which, along with Indonesia, has a Muslim majority population.
"We're going to be on Lebanese territory ... We're not going to be on Israeli territory," Foreign Minister Syed Hamid Albar said.
As Lebanese troops continue to move into the south of the country as part of the UN ceasefire, mass burials are being held for those killed during the past month.
Near the morgue in Tyre, 138 coffins were being dug up from a temporary mass grave to give to relatives for a proper burial.
In Qana village, where 28 people were killed in an Israeli air strike, relatives were gathering for a mass funeral.
Lebanese troops were welcomed as a "positive sign" by residents as they arrived in the devastated town of Khiam, close to the Israeli border.
"We hope that the two parties, Hezbollah and the Lebanese army, have an agreement on this [deployment]," resident Ahmed Zoghbi said.
Israel says it has now withdrawn from two-thirds of its positions in southern Lebanon, including the port city of Tyre and villages of Qana, Hadatha and Beit Yahoun.
Under the terms of the UN ceasefire resolution which ended the month-long conflict between Israel and Hezbollah, the expanded UN force should work alongside the Lebanese army in the south to keep the peace.
Each force should eventually number 15,000.