Analysts say the primaries are a good indicator of who may win the presidential elections later this year.
With 93% of the votes counted, governing coalition candidate Daniel Scioli had a 14-point lead over his conservative rival, Mauricio Macri.
The first round of the presidential election will be held on 25 October.
President Cristina Fernandez de Kirchner, who has been in power since December 2007, will not be able to stand again as the constitution limits presidents to two terms in office.
She was preceded in office by her late husband, Nestor Kirchner.
Their combined 12 years in office have been dubbed "the Kirchner era" and opposition candidates have been campaigning on a promise of change.
Mr Scioli, who is currently governor of Buenos Aires province, is the only candidate for the governing Front for Victory coalition.
His main rival is Buenos Aires mayor Mauricio Macri of the conservative Cambiemos (Let's Change) coalition.
With 93% of the votes counted, Mr Macri had won 24.4% compared to Mr Scioli's 38.3%.
Third was Sergio Massa, a congressman who broke away from the Front for Victory coalition to form his United for a New Alternative party.
Voting in the primaries is compulsory and is not restricted to party members but open to all those eligible to cast their ballot in the presidential polls.
Whoever wins is therefore seen as a favourite for the presidential polls on 25 October.
The primaries were introduced in 2009 to cut down on the number of candidates running in the presidential elections with contenders having to win a minimum of 1.5% to be eligible to stand in the first round on 25 October.
If no candidate wins 45% of the vote or 40% with a 10-point margin over the second-placed person, a second round will be held on 24 November.
Whoever wins will need to tackle a high inflation rate, which independent analysts estimate at 30%.
Mr Macri is campaigning on a promise to quickly free the markets from restraints introduced by President Fernandez while Mr Scioli advocates gradual change.
The presidential candidate for Argentina's governing coalition has won a comfortable majority in primary elections held on Sunday.