Mr. Zamora, citing preliminary returns, had asserted that the elections made Convergence the third-strongest political force in the country.
Dr. Berisha said preliminary returns indicated that the Democrats had won 72 seats.
The mood picked up for a few hours as preliminary returns, projected on large screens, showed the race to be close.
Nationally, the main opposition Fine Gael party held its vote at about 25 percent, according to official preliminary returns.
It has an area of 22,285 km and a population of 15,563,000 at the 2011 Census (preliminary returns).
The Central Elections Commission announced some very partial preliminary returns Monday night, then said the next day that it was ready to start the final official count.
You've got die first edition with the preliminary returns and you eat while one of you reads the figures aloud.
After an election held under American supervision, preliminary returns gave the opposition 20 seats in the Assembly to the government's 13.
According to preliminary returns, Ms. Messinger was just 2,533 votes short - out of 396,115 cast - of achieving the 40 percent needed for victory.
Mr. Lieberman beat Mr. Lamont by 7 percentage points, according to preliminary returns.