On Saturday, hundreds of mourners paid homage to the teenagers by holding a peaceful procession in the north-eastern suburb, which has a large immigrant population.
Tough response
The authorities have denied rumours that policemen were chasing the two boys, who were electrocuted on Thursday after entering an electricity sub-station.
Flowers now lie near the spot where Ziad, aged 17, and Banou, 15, died.
An official investigation into the boys' deaths is under way.
A third young man is seriously ill in hospital.
The BBC's Alasdair Sandford in Paris says many in the suburb do not believe the authorities' account that the two boys were not being chased by police.
Mr Sarkozy has promised to send special police units into difficult suburbs around France to stamp out violence.
Residents will be given "the security they have a right to", he said while speaking to senior police officers in Clichy.
He promised to find out who had hurled one or more tear gas canisters into a mosque on Sunday night, but added "that does not mean that it was fired by a police officer".
Rumours that the tear gas was thrown by the police into a place of worship fuelled the unrest.
Mr Sarkozy also met the president of the Muslim community in the Clichy area.
Local people in Clichy have accused Mr Sarkozy of heightening tensions by using inflammatory language.
During Saturday's march in memory of the dead teenagers, there were calls for the government to tackle discrimination against immigrant communities such as theirs.
Mr Sarkozy told police on Monday that "for 30 years the situation has been getting worse in a number of neighbourhoods".
"It's not a story that's three days, three weeks or three months old," he said.