Tamara Pletnyova, head of the family, women and children's affairs committee, argued that even if these relationships led to marriage, women or their children would inevitably be taken overseas by the man.
She said women who had babies with foreigners around the time of the 1980 Olympics in Moscow often "suffered" as single mothers. She added that, even if Russian women get married to their foreign partners after giving birth, they could end up living overseas with their spouses and have no idea how to return home.
Asked if the World Cup could boost Russia's birth rate - a key goal for President Vladimir Putin - Pletneva replied: "We should be giving birth to our own children". "They've suffered in the past, since the Soviet period".
Children who are mixed-race are likely to be brought up in one-parent families, she warned.
'Will there still be girls who will date foreigners and then have children from them Perhaps there will be some, but I am hoping not'. "I'm not a nationalist, but still", she added. They are being dumped and this is it.
She said that children risked being "abandoned and just left with their mother;" or, alternatively, being taken overseas by their fathers, urging women to marry "Russian citizens".
"Even if they marry, they move her overseas, then she does not know how [to return] from there", Pletnyova, who is known for her conservative remarks, told the Govorit Moskva (Moscow Speaks) radio station on Wednesday. "I know that the children suffer as well, and then they are abandoned and stay here with the mother".
'I would have liked people in our country marry for love, regardless of nationality'.
Pletnyova concedes that if Russian women simply can't control themselves, they should at least have sex with visitors of the same race.
However, her comments drew both criticism and ridicule.
Meanwhile, companies involved in this year's World Cup - including Federation Internationale de Football Association and Russian Railways - are having employees take classes to learn how to smile and make tourists feel more welcome.
'We're not in America or Europe.
Pletynova has been an MP since the first post-Soviet parliament in 1993.