Greece says it is almost certain to veto Macedonia's bid to join Nato, following Macedonian portrayals of the Greek prime minister as a Nazi.
The two countries are also in dispute over the name "Macedonia" for Greece's northern neighbour.
Time is running out for a solution before the Nato summit in Bucharest, which opens on Wednesday evening.
US President George W Bush had hoped to invite Macedonia to join Nato, along with Albania and Croatia.
Athens is deeply offended by posters that have appeared in Skopje, which have the swastika superimposed on the Greek flag, as well as a magazine cover which depicts Prime Minister Kostas Karamanlis as an SS officer.
And the Greeks feel insulted by recent images of their neighbour's prime minister laying a wreath by a flag showing a map of Greater Macedonia, which includes parts of Northern Greece.
Greece's foreign minister, Dora Bakoyannis, says the dispute is not just over a name.
She says the government in Skopje regards the Greek province of Macedonia as occupied territory and has refused to remove such claims from textbooks speeches, maps and national documents.
Athens and Skopje have failed to reach an agreement on a new name for the Former Yugoslav Republic of Macedonia, and Greece's stance remains - no deal, no invitation.
Greece is under huge pressure to back down.
The Americans say a dispute over who are the descendants of Macedonia's legendary king Alexander the Great cannot be allowed to derail Nato's expansion.
Other Nato allies are worried that closing the door on Skopje could lead to the break up of the country along ethnic lines between Slav Macedonians and the Albanian minority.
But compromising on what most Greeks regard as an unsatisfactory name would be political suicide for the Conservative government of Mr Karamanlis, and so the use of Greece's veto looks inevitable.