The scandal has drawn widespread attention outside France and overshadowed Mr Hollande's visit yesterday to Holland, his first foreign trip since the report.
He said Valerie Trierweiler was "doing better" but refused to respond to another question about his personal life.
Ms Trierweiler was taken to hospital with what aides called extreme shock after the affair claims this month and sources close to the president has confirmed his relationship with her is over.
Mr Hollande has never married and the reported affair with actress Julie Gayet has prompted questions about whether Ms Trierweiler will stay in the state-financed office of First Lady.
The couple have lived together since 2007, after Mr Hollande ended his long-standing relationship with Segolene Royal, with whom he has four children.
The president said last week he would make a decision on the First Lady's status before a planned trip to America next month. Neither Mr Hollande nor Ms Gayet has denied the alleged affair.
A smiling Mr Hollande met King Willem-Alexander and Queen Maxima at the royal palace Noordeinde in The Hague before a series of talks with Dutch politicians.
It was the kind of high-profile trip on which he would normally have been accompanied by his First Lady.
If her relationship with Mr Hollande is over, she may be forced to move out of the Elysee Palace.
In her first public comment on recent events, she sent a message on Twitter, saying: "Thank you from the bottom of my heart to all those who sent messages of support."