The Hungarian Boxing Association said in a statement it “objects to the appearance of the Algerian competitor” in the Olympics.
Khelif beat Angela Carini in the first round of competition as the Italian abandoned their bout after 46 seconds.
Carini said on Thursday she ended the fight to “preserve her life”, but apologised to her opponent on Friday for not shaking hands.
In its statement, the Hungarian Olympic Committee (MOB) said it wanted to protect “the right of female competitors to equal opportunities and fair competition”.
“The president of the MOB initiated an immediate consultation with the IOC sports director in order to clarify the situation,” it added.
The Russia-led International Boxing Association (IBA), which carried out the tests last year, said Khelif “failed to meet the eligibility criteria for participating in the women’s competition, as set and laid out in the IBA regulations”.
Khelif has always competed in the women’s division and is recognised by the IOC as a female athlete.
“The Algerian boxer was born female, was registered female, lived her life as a female, boxed as a female, has a female passport,” IOC spokesperson Mark Adams said on Friday.