Italy has said it would be willing to lead a force to police the ceasefire in southern Lebanon.
A small number of French troops have arrived in Lebanon
But Foreign Minister Massimo D'Alema warned his country could only fulfil its offer if Israel respected the truce, now in its ninth day.
Israel says it shot three suspected Hezbollah fighters in south Lebanon late on Monday, although this was denied by the militant group.
The incident shows just how fragile the ceasefire is, correspondents say.
Italian Prime Minister Romano Prodi said his country was willing to lead the planned international force - a task that was initially expected to go to France.
He said UN Secretary General Kofi Annan would make a decision by the weekend.
Mr Annan is to meet European Union foreign ministers in Brussels on Friday to discuss Europe's contributions to the force.
Mr D'Alema said Italy could offer up to 3,000 troops - the most substantial offer so far.
But in a newspaper interview, he stressed that Italy wanted a "renewed commitment ... to respect the ceasefire" from Israel.
"It is right to demand that Hezbollah give up its weapons but we cannot send our soldiers to Lebanon while the Israeli armed forces continue to fire," he told La Repubblica, ahead of a visit from Israeli Foreign Minister Tzipi Livni later this week.
Italy's "positive role" has been welcomed by the Lebanese cabinet, Information Minister Gazi Afridi said.
Israel has also said it would be happy if Italy led the force.
But Italy's offer appears to be conditional on an agreement being reached on a new UN resolution, AFP news agency reported.
The agency quoted Mr Prodi as saying a new resolution should provide "a specific mandate, specific contents and a very clear definition of the alliances".
Turkish Foreign Minister Abdullah Gul said his country was still undecided on joining the UN force.
After a meeting with the Syrian President Bashar al-Assad in Damascus, Mr Gul said Syria would support any Turkish involvement.
But he said his country wanted clarification on the UN force's mandate before deciding to commit troops.
Turkey is the only Muslim member of Nato and has good relations with both Israel and its Arab neighbours.
It has been under pressure from both the European Union and the US to send a contingent to Lebanon.
UN Resolution 1701 calls for 15,000 troops to be deployed to uphold the ceasefire between Israel and Lebanon.
But some countries have been reluctant to commit troops because they fear their soldiers might get drawn into conflict if they are required to disarm Hezbollah directly.
France had been expected to lead the peacekeeping force, but offered only 200 troops after expressing concern about the lack of a clear mandate.
Deputy UN Secretary General Mark Malloch Brown said he was still hopeful that European countries, including France, would commit more forces.
He also rejected Israel's view that countries it has no diplomatic relations with - such as Malaysia and Indonesia - should be excluded from the force.
Mr Malloch Brown said Israel should have confidence in the force but that this did not give it the right to veto contributions from some countries.
Israeli troops remain in southern Lebanon and both sides accuse each other of violations.
The Israeli military said it shot at three suspected Hezbollah fighters late on Monday, killing two, in south Lebanon near the border with Israel.
Hezbollah called the report "entirely baseless".