35 women were detained in Tehran on Thursday after trying to attend a soccer match, which was attended by FIFA's president Gianni Infantino.
He has the power to suspend the Iranian Football Federation and prevent Iran from taking part in the World Cup if the ban on women attending matches is not lifted.
The 35 Iranian women detained at the football match have received an outpouring of support on social media.
"It's very clear that politics should stay out of football and football should stay out of politics", Infantino said at a joint news conference in Tehran with Iranian Sports Minister Massoud Soltanifar.
The FIFA president then went to watch a derby match between Tehran rivals Persepolis and Esteghlal.
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Later on, Infantino met with Iranian President Hassan Rouhani. "Hence, my appeal to the Iranian authorities; open the nation's football stadiums to women".
However, Infantino also added that he was reluctant to be heard as "criticizing anyone".
Mr Infantino had been speaking to reporters about a two-year dispute between Saudi Arabia and Iran.
One female football fan tweeted: "They did not let us in the stadium, took pictures and videos of us and threatened to arrest us".
There were activist calls for women to try to attend the 1 March game in order to attract the notice of visiting Federation Internationale de Football Association officials and draw attention to the extremely conservative social rules that impinge on women's rights in the country.
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Iranian women are now banned from attending games across the Middle East country.
But Infantino said he was more interested in engaging in a "dialogue" rather than ultimatums.
In phone calls from Iran to VOA Persian's Straight Talk show on Thursday, one man said that if women went to football stadiums, they would find their dignity violated by men shouting foul language and acting aggressively.
Iranian women watch the Iranian men's basketball team play Iraq in a FIBA World Cup Asian Qualifier at Azadi Indoor Stadium in Tehran, Feb. 25, 2018.
Middle East editor Alan Johnston wrote the female football fans wanted to attract the attention of the most powerful man in world football in an article for the British public broadcaster. News site IranWire quoted him last December as telling students during a lecture that the presence of women in stadiums "inevitably" leads to morally corrupt acts.
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Any passengers whose flights have been cancelled should not come to the airport. "Today remains challenging and there will be disruption".
OpenStadiums - a movement of Iranian women - has written an open letter to Infantino calling on him to use his power and influence to end the ban.