The condition of an Egyptian man said to have attacked soldiers with a machete at France's Louvre museum has deteriorated, authorities said.

The suspect has been in hospital in Paris since he was shot four times by soldiers on Friday after injuring one in an underground mall that is part of the Paris museum complex.

He allegedly shouted "Allahu akbar!" while rushing towards the troops.

The man, identified as Abdullah al-Hamahmy, was put under supervised custody at the European Hospital Georges-Pompidou on Saturday after his condition improved.

But the Paris prosecutor's office said on Tuesday night that the custody was "lifted" after his condition "sharply deteriorated during the day".

His current condition was "incompatible" with keeping him in custody, it said.

After remaining silent during his first two questionings, the suspect had started to answer investigators' questions on Monday.

He confirmed his name as Abdullah al-Hamahmy and identified himself as a 29-year-old Egyptian citizen, the prosecutor's office said.

During the questioning, the suspect gave "his first version of the facts", the office added, but gave no details.

Soon after the attack, Egyptian officials identified the suspect with his full name, Abdullah Reda Refaie al-Hamahmy, but said he was 28.

With its custody now ended, the prosecutor's office said the case was no longer under its supervision and had shifted to the authority of counter-terrorism investigating magistrates.

The office said it would ask the investigating judges to file preliminary terrorist charges against al-Hamahmy once his condition had improved enough.

It said it was seeking charges of "attempted terrorist murders" and "terrorist criminal conspiracy".

The Louvre was closed after the attack, but reopened over the weekend.

The suspect's father, Reda Refaie al-Hamahmy, said his son had lived in Dubai for the past five years and was employed by a law firm.

Egyptian officials have said local security agencies were gathering information on al-Hamahmy to help establish if he was a member of any militant groups or had been radicalised.

Egyptian Investigators are examining his social media accounts and information gathered will be shared with French authorities, they have said.