'I accept Madonna's invitation with pleasure,' Le Pen told AFP.
Madonna, who in the past has demonised Le Pen on stage by portraying her with a swastika on her head, made the unusual overture during a French television interview late Monday.
'I would like to sit down and have a drink with her. I want to understand where she's coming from,' she said on the network Canal+.
The American singer, who superimposed the swastika on video of Le Pen's face during a 2012 Paris concert, only last week called Le Pen's National Front party 'fascist'.
In the interview she conceded: 'Maybe I misunderstood Marine Le Pen. I'm not sure. I don't want to start a war. I want peace in the world.'
The unusual gesture appeared an attempt to calm a confrontation with Le Pen, who had threatened a lawsuit over the swastika stunt.
The French far-right leader, who has been striving to soften the image and broaden the appeal of the party she took over from her father Jean-Marie Le Pen, embraced the singer's invitation.
'I appreciate people who make overtures in good faith,' Le Pen said.
Madonna, 57, has rarely shied away from controversy, be it about overt sexuality or political commentary. As recently as last week, on French radio, Madonna claimed 'it feels like Nazi Germany' in Europe because 'anti-Semitism is at an all-time high' in France and elsewhere on the continent.
The diva also told the Europe 1 radio station she had received 'a lot of criticism and threats from Marie (sic) Le Pen' and the 'fascist' National Front.
During the Canal+ TV show, she also met and hugged one of the cartoonists who survived the January 7 massacre at the offices of Charlie Hebo, the French satirical newspaper. And the entertainer sang a couple of songs from her new album, 'Rebel Heart', that she is promoting ahead of a global tour.
Madonna's on-stage tumble at the Brit Awards, when a cape she was wearing failed to detach on cue and brought her crashing down steps, was raised early in the show.
The interviewer quoted a Chinese proverb that says 'the biggest difficulty is not how you fall, but to get up each time that you fall'.
That earned a surly response from Madonna. 'Is it going to be a whole night of these jokes?' she asked.
From AFP Via Yahoo! News