Reflecting the delicate nature of Balkan politics after the wars that split Yugoslavia, the president of Macedonia also stayed away after the car of his prime minister was hit with eggs and its flag burned in Tirana during a visit last week.
Ethnic Albanians from across the region celebrated in the national colours of red and black with a 14 tonne cake and bushy moustaches to honour the founding fathers.
Albanian Prime Minister Sali Berisha's remarks were in a text he sent to a museum on Tuesday evening to mark the 100th anniversary of Albanian independence from Ottoman rule and honour the founder of modern Albania, Ismail Qemali.
In the statement, he referred to "the Albania of all the Albanian lands from Preveza to Presevo, Skopje to Podgorica".
Preveza is part of the northern Greek province of Epirus, where some ethnic Albanians lived before World War Two. Greece is Albania's second trading partner and its biggest foreign investor. Both countries are NATO members.
Skopje is the capital of Macedonia and Podgorica the capital of Montenegro, both close to Albania. Presevo is in southern Serbia close to the border with ethnic Albanian-majority Kosovo.
"Such comments do not help in fostering a climate of friendship, trust and good-neighbourly relations between the two countries," the Greek Foreign Ministry said, adding Foreign Minister Dimitris Avramopoulos had scrapped his trip over the matter.
Berisha's office sought to play down the spat, saying he was referring to the "historical context of a 100 years ago" and that did not "express any territorial claim to our neighbours in the south, north or east".
Former foreign minister Paskal Milo, a historian, also sought to play down its impact, saying whoever heard Albanians celebrating should not misinterpret their comments.
Moustaches
Nationalists in Greece and Albania had long made claims on their respective lands. But relations between the Balkan neighbours have significantly improved since they signed a friendship treaty in 1996.
Last month, however, Greece had to apologised to Albania for placing its red flag depicting a black, double-headed eagle, upside down during a visit by its foreign minister to Athens.
Albanians are by far the largest group of foreign workers in Greece - estimated at up to 800,000 in a country of 11 million people - and have been among the first to feel the hit from the deep Greek economic crisis.
Hundreds of thousands of ethnic Albanians from Kosovo, Macedonia and Montenegro partied along with Albanians in the capital Tirana and the coastal town Vlore, where independence was declared.
Some scooped chunks up of the giant cake with both hands and tossed pieces to friends and into the air.
In Kosovo, some sported moustaches to mark the day.
"I have grown my moustache to respect the men who declared independence in 1912 because most of them had moustache," said Kosovo Albanian Kreshnik Berisha in Pristina.
Albania turned into the battlefield for the belligerents of World War One and only began functioning as a state in the early 1920s.
The self-proclaimed King Zog brought order and started reforms but also led the country into the influence of Italy and he fled shortly before the Italians occupied Albania during World War Two.
Stalinist hardliner Enver Hoxha later established an isolationist communist rule for more than four decades until communism crumbled in 1990, causing an exodus of Albanians.
