"A law that could provoke debates and reactions aims to put an end to discrimination and will allow civil unions between same-sex persons," Berisha said in a government statement.
Berisha said there was "a certain hostility towards minorities" in Albania and called on citizens to respect "the standards of other European countries."
Albania, a secular state with a Muslim majority, revoked in 1995 a law that punished people with up to 10 years imprisonment just for being homosexual.
The former hardline communist country has an estimated gay population of several thousand, most of whom live secret lives without openly proclaiming their sexual orientation.
In recent years, several non-governmental groups have been formed to protect gay rights in Albania, which also has a large Catholic and Orthodox Christian population.
"We will firmly oppose that law," Islamic leader Selim Muca told AFP.
A spokesman of the Catholic Church in Tirana said: "We cannot accept that law, we are categorically against it."
Albania's parliament is expected to debate the legislation in coming weeks. If adopted, it would make the country the first in the region to legalize gay marriage, according to human rights groups.
Berisha, who leads the right-wing Democratic Party that won June 28 elections, is regarded as the man who ended almost 50 years of isolation under the rule of communist dictator Enver Hoxha.
His previous government formally submitted Albania's application to join the European Union two weeks before the polls.