The coalition government of Sali Berisha, the country's prime minister, won 75 of parliament's 140 seats on June 28, but the socialists have said that the result was manipulated.
They have boycotted parliament to press their call for a recount, a demand that Berisha has said is illegal.
'Battle for transparency'
Rama on Saturday called for protests be held throughout the country, urging Albanians to erect a "human barricade against the government".
"Protesters [have boosted] our battle for transparency and expressed their unshaken will to stop the economic ruin," he said.
Meanwhile, thousands of government supporters gathered in another square nearby, in a festive mood, carrying placards "Celebrate May 1, with Yes to Europe".
Carrying Albanian and European flags, they listened to a brief message from Berisha, saying that Albania "is on the way to its European future".
"Let's invite every citizen of this country to continue on the road toward Europe," he said.
Hundreds of police, including anti-riot units, were deployed between the two groups to avoid clashes.
Albania submitted its candidacy for EU membership in April last year and hopes to quickly obtain the lifting of visa requirements for its citizens to travel throughout the Schengen zone, which covers most EU countries.
But the political deadlock has undermined its EU ambitions, as European officials have warned the two sides they must find a solution to the stalemate.