"They indeed do not want this and they announced they will close their borders if this takes place," Finland's Erkki Tuomioja said after meeting Walid Al-Moualem, Syria's foreign minister, in Helsinki on Wednesday.
Israel has asked the UN to station peacekeeping troops at Lebanon's border-crossings with Syria so that Hezbollah cannot break the ceasefire by importing weapons.
Syria is the only country which has an open border with Lebanon. Lebanon also borders Israel but the two countries do not have diplomatic or trading relations as Beirut does not recognize the existence of Israel.
The UN is trying to put together a force of 15,000 to monitor a truce in southern Lebanon after a month-long war between Israel and Hezbollah, the Shia Muslim militia. Finland holds the European Union's revolving presidency.
Bashar Al-Assad, the Syrian president, had said on Tuesday that the deployment of international forces on the Lebanese-Syrian border would constitute a "hostile position".
Fuad Siniora, Lebanon's prime minister, has responded to Syria's threats by saying that Lebanon was capable of taking care of itself.
"I have heard the remarks of the Syrian president and I respect his opinion but Lebanon acts with all means at her disposition to preserve her sovereignty, her independence and her interests," Siniora said on Wednesday.
Relations between Lebanon and Syria must be based on "mutual respect" because "we have no interest in being in disagreement with Syria while Syria has no interest in being in disagreement with us", he said.
Thousands of Syrian soldiers were based in Lebanon until 2005. They left after over a million Lebanese rallied in central Beirut to call for their departure.
Many Lebanese believe that Syria has used Hezbollah - which it helps fund and arm - to fight a proxy war against Israel in the hope of pressuring Israel into returning to Golan Heights which it captured from Syria in 1967.
If Syria closes its border, Lebanon would find it even more difficult to recover from the recent conflict.
Not only would trade would be harmed but the small country would also have to import its food, building materials and other goods exclusively by air or sea.
UN troop plea
The UN has continued trying to persuade countries to contribute peacekeeping troops to enforce and monitor the ceasefire between Israel and Hezbollah southern Lebanon.
EU ambassadors and military experts met for more than four hours in Brussels on Wednesday to prepare for a meeting on Friday of ministers and Kofi Annan, UN secretary-general, who wants Europeans to play the lead role in the force.
So far only Italy has agreed to contribute substantial numbers of soldiers - up to 3,000 ground troops.
France, which initially wanted to lead the UN mission, has only offered 200 non-combat troops to support the UN Interim Force in Lebanon (Unifil).
However, after meeting with Tzipi Livni, the Israeli foreign minister, in Paris, Dominique de Villepin, the French prime minister, said France might send more soldiers in Lebanon if the UN gives its soldiers a wider mandate to defend themselves.
"Today we're the country that's the most committed and present on the ground. We want to go further once conditions are fulfilled," Villepin said.
"It is extremely important for France - with our strong experience in Lebanon, with international experience in other arenas - that all guarantees can be supplied for an effective deployment of Unifil on the ground," he said.
The UN has hoped to have 3,500 extra troops on the ground by the end of August.