The leading contender for France's centre-right presidential nomination, François Fillon, is facing tough questions over his stance on abortion and sex discrimination, reports the BBC.
His rival, fellow Republican Alain Juppé, has urged him to "clarify his position" on abortion.
Meanwhile, a party colleague restated claims he denied her a ministerial post because she was pregnant.
Supporters will choose between Mr Fillon and Mr Juppé 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, Mr Fillon took a clear lead with 44.1% while Bordeaux mayor Mr Juppé 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 Mr Fillon's stance on abortion.
Mr Juppé claimed his rival had gone back on a previous statement affirming that abortion was a "fundamental human right".
Mr 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."