The opposition, gathered in a large coalition behind the conservative Democratic Party's leader Sali Berisha, stood at 34.1 percent.
The Socialist Party, which went to the election on an ambitious promise of EU membership for Albania within five years, can thus ensure its own majority, something it succeeded with even in 2021.
An election victory would mean a fourth term for 60-year-old Rama, who took over the prime minister's post from Sali Berisha in 2013.
Voter turnout stopped at 42.2 percent, around 4 percent lower than last time, according to the Albanian Election Authority.
A final result is expected on Tuesday.
