Kasereka, a former senior army officer, says he has government support to battle against the forces of General Laurent Nkunda, who took up arms three years ago for his Tutsi ethnic group.
Nkunda and officials of the Tutsi-dominated government of Rwanda, which borders DR Congo, accuse DR Congo of supporting the FDLR.
Joseph Kabila, DR Congo's president, denies the accusation.
Rwanda has twice invaded DR Congo in pursuit of Hutu rebels it blames for its 1994 genocide, in which 800,000 Tutsis and moderate Hutus were killed.
The second invasion sparked a 1998-2003 war in DR Congo which claimed more than 4 million lives, mainly due to disease or hunger.
Last week, Mai Mai fighters attacked Bunagana, a town held by Nkunda's forces on the eastern frontier with Uganda, triggering a series of counter-attacks against government troops.
The violence forced thousands of civilians to flee and prompted the army to give Kasereka an ultimatum to surrender.
DR Congo's army has fought Nkunda's forces since August, when his men abandoned a January peace deal and pulled out of mixed government brigades.
Kabila has sanctioned an new army offensive against Nkunda, who has not met a pledge to surrender a part of his fighting force, estimated at around 4,000 men.
Aid agencies fear a new offensive against Nkunda will worsen a humanitarian crisis in North Kivu that has so far prompted 370,000 people to flee their homes this year.