Qatar's soccer governing body said on Tuesday that Abdurisag had an exchange of words "in the heat of the moment" where he was the victim of racial slurs.
New Zealand said on Monday that their defender Michael Boxall, of Samoan heritage, had received a "significant racist slur" from an opponent during the Gold Cup warm-up match in Austria.
"In any case, the QFA takes the allegations incredibly seriously and stands against racism in all its forms," QFA added in a statement.
"The experience of racism should never be trivialised and remains a serious problem within the game.
"The QFA encourages the international football community to do more to tackle racism and discrimination on and off the pitch."
New Zealand's soccer governing body said on Monday that it will contact FIFA about protecting players from racism following the incident at the match.
It was one of two games to be abandoned on the day following allegations of racism.
Ireland's FA said its under-21 team had abandoned their match against Kuwait's Olympic side after a Kuwait player used racist language towards an Irish substitute.
Racism has dominated football headlines in recent months.
FIFA president Gianni Infantino announced an anti-racism committee led by Real Madrid forward Vinicius Jr, who has been victim of racist abuse in Spain's LaLiga.
