Army reinforcements have been sent to eastern Democratic Republic of Congo, where an offensive is planned against a renegade general's forces.
Gen Nkunda says he is protecting DR Congo's Tutsi community
General Laurent Nkunda rejects Monday's ultimatum to disband his forces.
He says he is willing to integrate his fighters into the army but insists his forces will not surrender under attack and has called for talks.
Negotiations have been rejected by President Joseph Kabila, who arrived in the eastern city of Goma on Sunday.
Some 1,200 of Nkunda's former fighters who have surrendered in recent weeks were paraded before President Kabila in the town.
More than 370,000 people have been displaced by the fighting since the start of the year in a growing humanitarian crisis.
President Kabila "is not going along with this negotiations story any more" and is going to stamp out rebel violence in the east, government spokesman Kudura Kasongo told Reuters news agency.
"The head of state, with his government, has decided to end this situation of insecurity," he added.
KEY FORCES IN THE KIVUS
FLNK - new group made up mainly of Congolese Mai Mai with some Rwandan Hutus formerly in the FDLR
FDLR - Hutu militia made up of former Rwandan soldiers and others who fled into Congo after the 1994 genocide
Gen Laurent Nkunda, with an estimated 5,000 soldiers
Monuc - UN Mission in the DR Congo
In an interview with the BBC, Gen Nkunda said that he had sent an envoy to meet President Kabila in Goma to try and avoid conflict and agree a ceasefire but he had not had a reply as yet.
"We cannot integrate (our army) under fire."
Earlier, Gen Nkunda said that if the government were to attack his stronghold of Mushaki, "we will defend ourselves".
He portrays himself as the defender of the local Tutsi ethnic minority against Hutu militants who have been operating in the area since fleeing Rwanda after the Tutsi genocide there.
"This is not normal and the government must accept to discuss this issue," he said.
"We ask the government to protect the Tutsi."
Both the army and Gen Nkunda accuse each other of breaking a recent ceasefire.
More than 300,000 people have sought shelter in camps
The fighting in North Kivu province has also raised concerns about thousands of displaced people who have been forced out of their homes.
Aid workers say people are heading further north into rebel-held territory, where they are now unable to reach them.
The army scored their first real victory against Gen Nkunda's forces with the capture of Karuba last week.
Government soldiers have taken up positions on the road south of Mushaki and on the surrounding mountains.
Gen Nkunda accuses the army of getting backing from Hutu militias. In turn, the finger is pointed at Rwanda for giving tacit support to Nkunda's men.
The tensions in the east are increasingly being seen as a proxy war between Rwanda's rival Tutsi and Hutu communities being fought on Congolese soil, says the BBC's Karen Allen in Goma.
A five-year war in DR Congo ended in 2003, but the 17,600 UN peacekeepers in the country (4,300 of them in North Kivu alone) have struggled to keep a lid on instability since then.
Commentators have warned that without a concerted effort to talk peace now, Congo could rapidly slide into its third war in a decade.