In the first year of his European Kart career (2001) he set a new record for the most fastest laps by a driver in a season (8) and had several wins before his serious injury. Born in Porto, Portugal, Rui was inspired by his father to begin racing, and drove in the 1997 Portuguese Kart Cup. In 1998, he moved on to the French Championship, finishing 12th overall and taking the rookie of the year award.
In the International Finals held at Estoril, Rui claimed the third place after taking pole position and the fastest lap of the race but was eventually disqualified
In 2000, Monteiro again competed in Portuguese Kart Cup, this time finishing 2nd in the championship after taking 4 wins throughout the season.
He also competed in a couple of one-off events, coming 2nd in the Spanish Super Prix.