Mr Hulot, a celebrity green activist who is one of Macron's most popular ministers, appeared close to tears in a television interview as he denied the "shameful" rumours.
"It hurts, when it's wrongful and unfounded. Yesterday my children were in tears," the 62-year-old said, describing the situation as "a nightmare".
Mr Hulot, a TV star who has forged a three-decade career as an environmental campaigner, won swift support from the presidency.
"As he has not been charged, there is no reason why he should resign," Mr Macron's office said.
Nicolas Hulot has reportedly been considering resigning in frustration over a lack of action on environmental issues. Source: AAP
Questioned on BFMTV about accusations from "the grand-daughter of a famous politician" dating back to 1997, Mr Hulot acknowledged that the woman filed a complaint in 2008 but said the case was dismissed.
"I was questioned at my own request and investigators very quickly concluded that there was nothing suggesting the case should be followed up," Mr Hulot said.
He was attempting to clear the air ahead of the publication of an investigation by a magazine that poses fresh problems for Mr Hulot, who has faced a difficult start to life as a politician.
The Ebdo weekly, due to publish an interview with his unnamed accuser on Friday, has described her accusations of being abused at one of his homes as "devastating".
Mr Hulot also denied suggestions that a former colleague had accused him of harassment.
"The answer is no," he told BFM. "The worst thing is that she has already been questioned by some of your colleagues and she gave the same answer."
He said he had not yet considered resigning, but added: "My family comes first, that's what will guide my decision."
Second minister under fire
The rumours dogging Mr Hulot emerged after Paris prosecutors reopened an investigation in late January into rape allegations against Budget Minister Gerald Darmanin.
A former call girl claims he pressured her into sex in 2009 in exchange for helping her clear her name in a legal dispute.
Mr Darmanin's lawyers have accused her of a "crude attempt to harm" the minister's reputation and said he was suing her for slander, and other ministers have rallied around their colleague.
France, like other countries around the world, has seen an outpouring of allegations of sexual assault and harassment in the wake of the scandal engulfing Hollywood mogul Harvey Weinstein.
Mr Hulot was among several figures Mr Macron brought in from outside politics to brighten his cabinet when the centrist newcomer came to power in May.
The environmentalist has regularly been reported to be on the brink of resigning, frustrated over issues including a decision to delay France's commitment to cutting its reliance on nuclear energy to 50 percent until after 2025.
After filing a declaration of his assets in December as required by ministers, press reports highlighted how the eco-warrior owned nine motor-engined vehicles, including an SUV.
