Ballon D'Or winner Karim Benzema called time on his tumultuous international career with France on Monday, a day after the defending champions World Cup final defeat to Argentina.

Benzema, who scored 37 goals in 97 appearances for France, had to withdraw from the World Cup squad before their first match in Qatar due to a left thigh injury he suffered in training.

In his surprise announcement, the 35-year-old Real Madrid forward said on Twitter: "I made the effort and the mistakes it took to be where I am today and I'm proud of it! I wrote my story and ours ends."

Benzema, who won the Ballon d'Or award for the world's best player in October, had been desperate to feature in this year's World Cup having not been selected when France became world champions in Russia four years ago.

He was frozen out of the France team for five and a half years because of his involvement in a blackmail scandal over a sextape involving his former teammate Mathieu Valbuena.

In a trial over the affair last year he was handed a one-year suspended prison sentence and fined 75,000 euros ($79,500).

For the Qatar World Cup, coach Didier Deschamps opted not to call up a replacement for a squad that included 23-year-old Kylian Mbappe.

Paris Saint-Germain forward Mbappe won the World Cup Golden Boot award with eight goals, including a hat-trick in Sunday's penalty shootout defeat by Argentina after the teams had drawn 3-3 at the end of extra time.

Benzema's departure, just three days before the first match against Australia, a 4-1 victory, was a turning point for the former Lyon player.

A knock to his left thigh in training while he was recovering from a niggling right thigh problem was estimated to need a recovery time of three weeks.

However, his hasty departure from Qatar had fuelled speculation of a rift between him and the rest of the squad as well as Deschamps. 

Asked about the case of the striker, not replaced and officially on the squad list until the end of the tournament, Deschamps had insisted "these things are not on my mind".

Benzema did nothing to dispel the misunderstanding with an array of mixed messages on social media. Amid encouragement for France, he also posted on Instagram before the final, "I'm not interested".

That message came after he rejected an invitation from French President Emmanuel Macron to attend the World Cup final.

Benzema, who scored on his senior debut in March 2007 against Austria, never tasted real glory with France, with his only title the 2021 Nations League. 

Freed from the weight of national duty, Benzema will now be able to devote himself to Real Madrid where he has won the Champions League five times and helped them to four Spanish titles.