Serbian President Boris Tadic has recognised the results of Montenegro's vote for independence, in the first official response from Serbia.
Boris Tadic said Serbia would always be a friend of Montenegro
"I accept the preliminary results reached by the referendum commission," Mr Tadic told a news conference.
Official results of Sunday's referendum in Montenegro put the pro-independence votes at 55.5% - just half a percentage point above the threshold for victory.
But a demand by pro-Serbian unionist parties for a recount was rejected.
"As you know, I was in favour of maintaining the common state... but as a democrat and president of a democratic country, I'm fully ready to accept the decision of the majority of the citizens of Montenegro," Mr Tadic said.
"Montenegro will always have in Serbia a reliable partner and friend," said Mr Tadic.
Later, Serbian Prime Minister Vojislav Kostunica - a nationalist and fierce opponent of Montenegrin secession - said Serbia was ready to acknowledge the results "once they become final".
"A referendum is an important event and the smallest doubt about its regularity has to be removed," Mr Kostunica told reporters in Belgrade, the Serbian capital.
A dispute over 19,000 votes in the capital Podgorica delayed announcement of the final results on Monday.
The referendum commission head Frantisek Lipka said the completed preliminary results showed 230,711 people, 55.5%, had voted for Montenegro to become an independent state.
He said 184,954 voters, 44.5%, had voted to remain with Serbia.
The results will be made final on Saturday after the expiry of a period in which they can be challenged. Turnout was 86.3%.
Several leaders of the pro-union bloc led by the Socialist People's Party signed a statement calling for a recount of the ballots.
But Mr Lipka dismissed their complaints, and the final result received the backing of European Parliament observers and the EU's Austrian presidency.
The European Commission said Montenegro could begin talks with the EU on closer ties and eventual membership.
"The European perspective is open to Montenegro," enlargement commissioner Olli Rehn said.
Serbia has seen its EU ambitions hampered by the failure to arrest key war crimes suspects, but Montenegrin Prime Minister Milo Djukanovic was optimistic about his nation's prospects.
"I am convinced Montenegro could be the next country from this region to join the European Union, after Romania, Bulgaria and Croatia, which are further along the process," he told Reuters news agency.
The process of disentangling Montenegro and Serbia is likely to involve detailed negotiations between the two governments, the BBC's Nick Hawton in Montenegro says.
The union of Serbia and Montenegro was all that remained of the federation of six republics that made up Yugoslavia before the independence wars of the 1990s.
The question of independence has proved divisive in Montenegro, with opponents arguing it will damage economic, family and political ties with Serbia.
Serb politicians, Orthodox church leaders and Montenegrins from the mountainous inland regions bordering Serbia broadly opposed secession.
However, ethnic Montenegrins and Albanians from the coastal area largely backed the prime minister and favoured independence.
The last time Montenegro was independent was nearly 90 years ago at the end of World War I, when it was absorbed into the newly formed Yugoslavia.