Thierry Solere, president of the organization commission of the primary, said former prime minister Francois Fillon took 42.8 percent of the first 690,000 votes that have been counted out of over 2.5 million ballots by late Sunday evening.
Alain Juppe was in second place with 26 percent and Nicolas Sarkozy in third place with 24.4 percent.
None of the other candidates managed more than 3 percent of the poll.
It was a large turnout for the first vote of its kind to be organized by France's conservatives. Candidates were previously designated internally. The change to the US-style primary has been widely regarded as a response to the rise of the far-right National Front (FN).
A second round vote is expected to be held next Sunday to decide between the two front-runners.
Rise of the populist right
The surprise vote for Britain to leave the EU this summer and Donald Trump's victory in the US election has served as a wake-up call in France, upending long-held assumptions and triggering fears, and hopes, that next spring's election will deliver a similar upset.
The chances of France's far-right leader Marine Le Pen running for, and possibly winning, the French presidency in 2017 have also apparently been boosted by Trump's election success.
The National Front (FN) leader has hopes that an anti-immigrant, anti-Muslim and anti-establishment sentiment can propel her to the presidency.
Former President Sarkozy hopes to pull back votes from the populist right, however, after calling for stricter immigration rules across Europe.
With the French left still divided, the outcome of the conservative primary will be crucial. The conservative nominee who emerges from next Sunday's runoff is tipped to go on to take the presidency in May.
Another unknown factor in Sunday's first round is the number of left-wing voters prepared to pay two euros ($2.10) and sign a declaration that they subscribe to "the values of the centre and the right" to vote in the right-wing primary. Those who did were expected to vote against Sarkozy and polls suggested a high voter turnout would benefit Juppe.
President Francois Hollande's is also yet to announce whether he intends to bid for re-election. On Wednesday, Hollande's former economy minister Emmanuel Macron said he would stand as an independent candidate.
cw/jm (AFP, Reuters)