Montenegro's pro-Serbian unionist parties have demanded a full recount after a referendum narrowly won by the pro-independence camp.
Opponents of independence said the economy would suffer
According to near-complete results, those favouring independence polled 55.4% in Sunday's vote - slightly more than the 55% required for victory.
Montenegro's electoral body delayed announcing final results because 19,000 votes are still in dispute.
If confirmed, the outcome will erase the last vestige of former Yugoslavia.
The question of independence has deeply divided Montenegro, with opponents arguing it will damage economic, family and political ties with Serbia.
"The preliminary results... should be re-checked and the ballots at all polling stations again recounted," a statement by the unionist bloc said.
It was signed by several leaders of the pro-union bloc led by the Socialist People's Party.
"We demand that at a certain number of polling stations, where an enormous increase of the turnout was registered, the signatures of voters in the register should be compared with their identity card signatures," it said.
The head of the referendum commission, Frantisek Lipka, had been expected to announce the final result on Monday evening, but he said there was still dispute over 19,000 votes from 37 polling stations in Podgorica.
It is not clear whether the commission would consider a late recount request.
Mr Lipka said earlier that about 5% of the votes were still to be counted, but he said they were not expected to affect the outcome.
Turnout was 86.3%.
The commission said the poll had been carried out according to rules agreed by both the pro- and anti-independence camps
One European Parliament election observer, Robert Evans, told the BBC that everything in the vote had satisfied their requirements.
EU foreign policy chief Javier Solana said he would respect the result.
Indications that the pro-independence bloc may have won the vote prompted celebrations in the Montenegrin capital, Podgorica.
The tooting of car horns filled the city and youths were seen waving the red and gold flag of the old Montenegrin monarchy.
Prime Minister Milo Djukanovic said earlier that the poll showed that "the independence of the country has been renewed".
He argued that an independent Montenegro - which has a population of fewer than 700,000 people - would have a stronger economy and be a better candidate for admission into the European Union.
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.
BBC South-East Europe analyst Gabriel Partos says Montenegro will have to wait for reaction from Serbia before the process of proclaiming independence gets under way.
Under their union's founding charter, Serbia will become the successor state, and Montenegro will have to apply for membership of the EU, United Nations and other international institutions.
Serbia will also lose direct access to the Adriatic Sea, and granting special rights of access will give Montenegro a strong position in forthcoming talks on dividing the union's assets, our correspondent says.
Montenegro's loose union with Serbia was established in 2003, replacing what was left of the former Yugoslavia.
Both sides were given the option of electing to leave the union after three years.
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.