Cufre has been capped 4 times for the Argentina national football team and was part of the country's squad for the 2006 FIFA World Cup.

Cufré moved to France in Summer 2006, joining Ligue 1 side AS Monaco[1] During his time at the club, he made 61 appearances and managed to score three goals.

On 16 August 2009, after a mini "soap opera," the Argentine wingback asked for – and was granted – his release due to a conflictive relation with Leonardo Madelón, the head coach at the time (though, personal reasons were officially cited).

[3] On 19 August 2009, he officially signed a contract with Croatian champions Dinamo Zagreb who had reportedly been persuading him to join the club since the summer transfer window opened.

[4] On 7 December 2011, same day he officially terminated his contract with Dinamo Zagreb, it was revealed that Cufré would be joining Mexican Club Atlas from Guadalajara.

On 30 June 2006, Cufré was red carded for violent conduct in an altercation following Argentina's loss on penalties to Germany in a quarter-final match.