Kabila came to power after the murder of his father Laurent-Desire Kabila by a bodyguard in 2001 during the Second Congo War
The "Bye-Bye Kabila" movement wants the president, who has been accused of delaying election preparations, to unconditionally stand down and rule himself out from staying in power.
"The people of Congo gathered today to inform the national and international community of the Bye-Bye Kabila campaign," Merveille Gozo, one of the organisers, told reporters.
An accompanying "peaceful protest" is planned for Friday to signal that it is time for Kabila to "enter history through succession", Gozo said.
Kabila came to power after the murder of his father Laurent-Desire Kabila by a bodyguard in 2001 during the Second Congo War, which ended two years later.
Elected in 2006, he went on to win a second five-year term in a 2011 vote decried as rigged by the opposition. Foreign official observers said the poll lacked credibility.
The constitution bars him from standing again but Kabila has never said he plans to step aside.
Police in Kinshasa on Saturday prevented a protest against Kabila from taking place, with officers occupying the square where the rally was planned.