The leading contender for France's centre-right presidential nomination, Francois Fillon, is facing tough questions over his stance on abortion and sex discrimination, BBC said on Tuesday.
His rival, fellow Republican Alain Juppe, has urged him to "clarify his position"
on abortion. Supporters are going to choose between Fillon and Juppe on Sunday.
It is the first time the centre right in France has used a US-style primary contest to select a candidate, ahead of the presidential election in April and May. In the first round of voting for the Republican nomination on Sunday, Fillon took a clear lead with 44.1% while Bordeaux Mayor Juppe received 28.5%. Five other contestants were knocked out.
As the campaign for the second round gathered pace on Tuesday, the candidates exchanged barbs over Fillon's stance on abortion.
Juppe claimed his rival had gone back on a previous statement affirming that abortion was a "fundamental human right".
Fillon, who is personally opposed to abortion but against revisiting its legal status, reacted with fury, saying: "I would never have thought my friend could stoop so low."
Another former colleague and defeated primary contestant Nathalie Kosciusko-Morizet - who now backs Juppe - has also renewed claims that Fillon denied her a ministerial post because she was pregnant.
Kosciusko-Morizet's remarks were first reported in 2013 in a profile by U.S. network NBC, when she said she had twice been turned down for ministerial posts when she was pregnant. During her second pregnancy, in September 2009, Fillon was prime minister.
Several French commentators have also made the point that Kosciusko-Morizet was not prevented from taking up a succession of posts in Fillon's government.
Fillon was also criticised by centrist leader Francois Bayrou for his proposed liberal economic reforms, which include cutting half a million public sector jobs and scrapping the 35-hour work week. Bayrou called them "dangerous".