Ms Bakoyannis hoped there was still time to reach a compromise
Greece has said it cannot support Macedonia's bid to join Nato, because of an unresolved dispute over its Balkan neighbour's name.
Greek Foreign Minister Dora Bakoyannis told reporters in Brussels that Athens backed inviting Albania and Croatia but could not consent to asking Macedonia.
The decision threatens to derail Nato's plans to invite all three Balkan states at a summit in Bucharest in April.
Athens objects to its neighbour taking the name of a northern Greek region.
It says the name implies a territorial claim on the region, which Macedonia denies.
Ms Bakoyannis made the comments in a speech handed to reporters after a meeting of Nato foreign ministers.
"Unfortunately the policy followed by the government of the Former Yugoslav Republic of Macedonia in its relations with Greece, particularly as concerns its intransigent stance and its actions of an irredentist and nationalist logic, do not allow Greece to take the same positive stance as in the case of Croatia and Albania," she said.
However, she said she hoped there was still time to reach "a mutually acceptable" solution in time for next month's Nato summit.
A UN envoy is currently trying to find a compromise for both countries.
Nato members are keen to extend the alliance into the Balkans, to stabilise the region after Kosovo's 17 February declaration of independence.
All three countries are backed by Washington and Nato Secretary General Jaap de Hoop Scheffer said they had worked hard on political and military reforms.
In the long run, he said, the only recipe for Balkan stability was their integration in Nato and the EU.
"I would like all three countries to join," German Foreign Minister Frank-Walter Steinmeier told reporters.
"A lot depends on the question of whether these two states are going to be able to come closer together in the coming weeks."
Dutch Foreign Minister Maxime Verhagen agreed the issue had to be resolved: "A name cannot be an objection for the accession of a country."
Requests by Ukraine and Georgia to get a road map for eventual membership are also proving divisive.
Although Nato members want to send a positive signal to the two former Soviet republics, some do not want to risk worsening relations with Russia, which are at their lowest point since the Cold War.
"In Russia we have a new president and I think the European Union wants to put its ties with Russia on another footing", Luxembourg's Foreign Minister Jean Asselborn said.
"We have to take the interests of others, not only the members of Nato, into account."
US Secretary of State Condoleezza Rice called on Nato members to help reinforce Canadian troops in southern Afghanistan.
Canada has threatened to pull out of Kandahar next year unless its Nato allies provide an extra 1,000 soldiers to help fight the Taleban. Dr Rice said Canada's Nato partners had "an obligation to deliver on that".
French Foreign Minister Bernard Kouchner said it was up to President Nicolas Sarkozy to decide whether the 1,900 French troops currently in the capital, Kabul, should be sent to the south or the east of the country.
Mr Kouchner also said that Norwegian diplomat Kai Eide had a good chance of taking up the role of the UN's special envoy in Afghanistan.
A previous candidate, Lord Ashdown, was rejected by Afghan President Hamid Karzai.