KINSHASA (Reuters) - Democratic Republic of Congo's M23 rebels have declared a ceasefire in their fight with the army, they said on Sunday, in a move they hope will advance peace talks with the government.

"We call on the facilitator of the Kampala peace talks to immediately put in place a mechanism to monitor the ceasefire," the rebels said in statement.

There was no immediate reaction from the army, which has pushed the rebels from all the towns they once controlled during a 20-month rebellion in North Kivu province.

Rebel fighters this week abandoned Bunagana, their last stronghold in the eastern province, and have withdrawn into the hills and forests around Congo's border with Uganda and Rwanda where the rebellion was launched last year.

On Friday, Uganda, which has led regional attempts to end the most serious rebellion since Congo's last war ended a decade ago, called for both sides to stop fighting. Heavy fighting has eased but the army said it shelled rebel positions on Saturday to encourage fighters to surrender.

Congo's government has dispatched senior negotiators to talks in Uganda but the army is keen to finish off the rebellion, the last in a series of uprisings led by Congolese Tutsis in the mineral-rich but unstable east.

(Reporting by Pete Jones; Writing by David Lewis; Editing by Robin Pomeroy)