Pakistani Prime Minister Shaukat Aziz has rejected an offer to resign by the tourism minister, who has been under strong pressure from hard-line clerics.
Nilofar Bakhtiar was pictured after a paragliding flight
Mr Aziz said that the minister, Nilofar Bakhtiar, was needed in the cabinet and she should carry on with her duties.
Last month, a fatwa was issued against her after she was pictured hugging a man following a paragliding flight.
Clerics said Ms Bakhtiar's behaviour was obscene. She said the photo was misleading and she had done no wrong.
Prior to her submitting her resignation as minister, Ms Bakhtiar had lost her job as president of the women's wing of the ruling Pakistan Muslim League party.
This was followed by a change in her portfolio to tourism from women's affairs.
The party said on Wednesday that her removal from the women's wing post was not connected with the hugging incident and it welcomed the prime minister's rejection of her resignation.
The BBC's Syed Shoaib Hasan in Islamabad says the affair reinforces the perception that Pakistan is increasingly coming under the shadow of Islamic fundamentalism - and reflects differing attitudes within the ruling party towards religious hard-liners.
The row began after the tourism minister made the jump in France in March to raise money for victims of the 2005 Kashmir earthquake.
Newspaper photographs showed her hugging her elderly instructor after the jump.
The hug that caused all the fuss
Hard-line clerics at the radical Lal Masjid (Red Mosque) in Islamabad issued a fatwa, or religious edict, condemning her behaviour, saying it violated Islamic morality.
At the time Ms Bakhtiar vowed not to be intimidated, but officials on Tuesday confirmed reports that she had handed in her resignation.
She was quoted as saying she had been hurt by the way the issue was sensationalised and that her parachute jump had been for a noble cause.
"We don't need to be intimidated by these people," she told Reuters Television in April. "I have no regrets... I would do it again happily if it helps the people of Pakistan."
Observers say the affair highlights a growing climate of extremism in Pakistan.
In February a female provincial minister was shot dead by a man who, police said, did not think women should be in politics.
The clerics who denounced the tourism minister have set up their own vigilante anti-vice squads in the capital.