Thousands of people turned out late Friday to greet Algeria's gold-medallist, who was the centre of a gender controversy at the Olympics on her way to the women's 66kg title.
Asked about a complaint that Khelif had filed with the Paris public prosecutor's office for online harassment, the boxer declined to elaborate.
"This is a day for celebration," she said. "I will address that question at the appropriate time."
According to US magazine Variety, billionaire entrepreneur Elon Musk and Harry Potter author JK Rowling have been named in the complaint.
Former US president Donald Trump, the Republican party's nominee in the 2024 presidential race, would also be part of the investigation, Variety said, citing Khelif's lawyer.
The boxer's coach, Mohamed Chaoua, said on Friday that Algerian President Abdelmajid Tebboune had taken a personal interest in Khelif's case.
He said Tebboune "has said we will not give up on our rights".
However, he too underlined that Khelif's return home was "a day and a time for joy" and that legal issues would have to be addressed in their own context.
Khelif won the women's 66kg final against China's Yang Liu in a unanimous points decision, having been the focus of intense scrutiny in Paris during the Olympics.
Together with Taiwan's Lin Yu-ting, who won the 57kg women's final, Khelif was disqualified from last year's world championships after they failed gender eligibility testing.
However they were cleared to compete in Paris, setting the stage for one of the biggest controversies of the Olympics.
Residents of Tiaret, a city of around 200,000 people 340 kilometres (210 miles) southwest of the capital, gave her a rousing welcome when she appeared with relatives aboard an open-top bus escorted by police.
"I was given a warm welcome today. Every Algerian has the right to rejoice and enjoy themselves," she said.
"Even the president is a fan of Imane Khelif, which proves that the state and the people are backers of sport," she added.
