Hollande described the demonstrations, in which US rocker Courtney Love was caught up, as "unacceptable violence in a democracy, in a country like France."
But Hollande, attending an EU leaders summit in Brussels, added: "UberPOP should be dissolved and declared illegal."
The service has been illegal in France since January, but the law has proved difficult to enforce and it continues to operate.
Around 3,000 cabbies took part in the strike yesterday, blocking access to the capital's Charles de Gaulle and Orly airports, and preventing cars reaching train stations around the country.
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Taxi drivers are furious at what they see as unfair competition from Uber, which puts customers in touch with private drivers at prices lower than those of traditional taxis.
Interior Minister Bernard Cazeneuve said after meeting taxi drivers' unions following a fraught day: "UberPOP is an illegal service, it must be closed down."
Until that was done, "the vehicles of UberPOP drivers should be systematically impounded when they are openly breaking the law", the minister said.
"Governing the country will never be done by the law of the jungle," Cazeneuve added.
Most cabbies heeded their unions' calls to return to work today, but around 40 die-hards remained at the busy Porte Maillot junction in western Paris.
"The drivers decided to keep up the action because we didn't get anything, only some things to regulate the (drivers) on the black market, which is in any case banned," said Khalid, a driver.
Yesterday, Love, Kurt Cobain's widow, was caught up in a confrontation near Charles de Gaulle airport. She tweeted that protesters "ambushed" her vehicle and "were holding our driver hostage". "This is France?? I'm safer in Baghdad," she added.