A government spokesman said the last remaining rebels had either fled across the border or surrendered and their weapons had been destroyed overnight.
The M23 have not publicly commented on the claim. Kinshasa earlier rejected rebel calls for a truce.
At least 800,000 people have fled their homes since the conflict began in 2012.
Last week, the UN special envoy to DR Congo, Martin Kobler, said the group was all but finished as a military threat in DR Congo.
The UN has regularly accused Rwanda and Uganda of supporting the M23 although both governments deny the allegation.
Last week government forces captured Bunagana, the main base of the M23 on the DR Congo-Uganda border.
But clashes continued on Monday and rebels shelled the town, killing four people. The violence prompted thousands of people to flee into Uganda.
The fighting came a day after M23 leader Bertrand Bisimwa called for a ceasefire to “allow the continuation of the political process”.
Bertrand Bisimwa urged rebel commanders to “ensure the strict observance of this order”.
But Kinshasa rejected the call.
Government forces backed by the UN captured the strategic hilltop of Mbuzi above Bunagana on Monday, then targeted the remaining hilltops where rebels were holed out.
African leaders meeting on Monday in the South African capital, Pretoria, called on the M23 rebels to declare publicly an end to their insurgency.
A statement released after the summit said if they did so a peace agreement could be signed in five days’ time.
Peace talks broke down last month in the Ugandan capital, Kampala, following two months of negotiations.
M23 rebel group, made up of army deserters who are mainly ethnic Tutsis, was named after a 23 March 2009 peace deal signed by the government and a former militia. The rebels accused the government of failing to live up to the terms of the agreement.
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