They had pushed towards Kigali from the north, north-west and north-east, to stop "ethnic cleansing" by government supporters who allegedly massacred more than 300 civilians of the minority Tutsi tribe last month, he said.
The mainly Tutsi RPF has fought a 28-month guerrilla war against the Hutu-dominated government of President Juvenal Habyarimana for the right of hundreds of thousands of Tutsi exiles who fled tribal bloodshed over the past 30 years to return to Rwanda.
The latest fighting, the heaviest since an internationally brokered ceasefire in August, prompted France to double its troops in Rwanda to 300 to protect more than 400 French nationals living in the tiny central African state.
Kagame repeated accusations that French troops were fighting alongside government forces.
He disputed the French troop figures, saying his intelligence reports indicated the presence of up to 1,000 French soldiers.
Kagame said the rebels were within 30 kilometres (18 miles) of the capital, but government forces still controlled territory further north behind the rebel advance positions including Ruhengeri and areas in the north-east.
"We've nearly doubled the area we hold," Kagame said. "We've suggested a ceasefire, but we won't return to our original positions. The other side must agree to sit down and negotiate new ceasefire lines."
"The only way to stop the massacres is to sit down and talk, but military force is needed to pressure Habyarimana into making concessions," he said.
AFP AFP SEQN-0155