A senior UN spokesman says it is now close to achieving firm promises of troops to make up the full peacekeeping force for southern Lebanon.
A small French contingent arrived in Lebanon on Friday
Edward Mortimer told the BBC that significant offers had been received from several Asian countries.
These are in addition to a commitment of up to 7,000 troops from European Union states.
The UN has agreed to deploy a force of 15,000 soldiers to maintain the ceasefire between Israel and Hezbollah.
Mr Mortimer said the UN was also hoping to get an offer of troops from Turkey, which he said would be very important given the country's history and geographical position.
The UN hopes to have some of the troops on the ground within a week, although the foreign minister of Finland - which currently holds the EU presidency - has said it will be two to three months before the whole force is deployed.
UN TROOP PLEDGES
France - leadership and 2,000 troops
Italy - 2,000 - 3,000 troops
Bangladesh - two battalions (up to 2,000 troops)
Malaysia - one battalion
Spain - one mechanised battalion
Indonesia - one battalion, an engineering company
Nepal - one battalion
Denmark - at least two ships
Poland - 500 troops
Finland - 250 troops
Belgium - 302 troops, later rising to 392
Germany - maritime and border patrols but no combat troops
Norway - 100 soldiers
UN Secretary General Kofi Annan said he had asked Italy to take over command of the force from France in February.
There will also be a strategic cell created to help provide military guidance to the troops on the ground, which will be based at UN headquarters in New York and led by an Italian general.
Israel has reiterated that it will not finally withdraw from southern Lebanon until the UN peacekeeping force is deployed.
In the meantime, EU foreign and security affairs chief Javier Solana has asked Israel to lift its air and sea blockade of Lebanon.
Speaking in Brussels on Friday, Mr Annan said that the plan would only work if the enlarged UN force, called Unifil 2, was "strong, credible and robust".
"More than half the force has been pledged today. Not only troops on the ground but we also got naval assets as well as air assets and when you put it all together Europe is providing the backbone to the force," he said.
Mr Annan said that the European force offered the possibility of a "durable ceasefire and long-term solution" to the Middle East crisis.
But our correspondent in Beirut says that with Hezbollah still firmly established across the border region and in no mood to give up its weapons, there is some scepticism about what an international force can achieve however tough its mandate.
The UN spokesman said that a political consensus was vital for the task.
"Everybody understands that the disarmament of Hezbollah as a whole is not going to be done by force," said Edward Mortimer.
"This is a matter which has to be agreed politically among the Lebanese."
French President Jacques Chirac, giving a joint news conference with German Chancellor Angela Merkel, told reporters that a force of 15,000 was unnecessary: "I don't know who mentioned this figure but it doesn't really make sense.
"So what is the right number, 4,000, 5,000 or 6,000? I don't know."
The UN was disappointed by the initial response of European nations to its calls for troops to enforce UN Security Council Resolution 1701 which ended the conflict.
France was criticised last week after offering just 200 extra troops to help bolster Unifil.
The issue has been complicated by Israel's reluctance to accept troops from mainly Muslim states which do not have diplomatic relations with it.