With results from 61 seats in the 71-member parliament confirmed, the SDL had 32 seats, the opposition Labour Party 25 and the United People's Party 2 while independent candidates won 2 seats.
"The SDL party and my colleagues feel honoured and privileged to be the government of the day for the next five years," Qarase said on Fijian radio on Wednesday.
"We will have a working majority and that is good enough.
Labour leader Mahendra Chaudhry immediately rejected Qarase's claim, saying "he hasn't won this election yet. Let's wait and see the final outcome".
Chaudhry's victory in the Pacific island's 1999 general election was followed by an armed coup by indigenous Fijians in May 2000 which toppled him from power.
Qarase had planned to offer amnesty to those involved in the coup, a move that angered military leader Voreqe Bainimarama.
Race is a central issue in Fijian politics with indigenous Fijians making up 55% of the population.
Ethnic Indians - mostly descendents of labourers brought to work on sugar cane plantations - are believed to represent under 40% of the population.
Results showed that many Fijians voted along ethnic lines with both groups winning all the seats reserved for them in parliament.