The rebel leader whose fighters have captured Goma, the biggest city in eastern Democratic Republic of Congo, has vowed to continue their offensive all the way to the capital, Kinshasa.

Corneille Nangaa, who heads an alliance of rebel groups that includes the M23, said their ultimate aim was to topple President Félix Tshisekedi's government.

Unconfirmed reports say the Rwanda-backed rebels are currently advancing towards Bukavu, the second-biggest city in the mineral-rich east, despite international calls for a ceasefire.

In a televised address after the fall of Goma, Tshisekedi said a "vigorous and coordinated response" was under way to recapture territory from the rebels.

"Be sure of one thing: the Democratic Republic of Congo will not let itself be humiliated or crushed. We will fight and we will triumph," he said on Wednesday evening.

The fighting has forced about 500,000 people from their homes, worsening an already dire humanitarian crisis, according to the UN.

On Thursday, Nangaa presented the rebels as the new administrators of Goma, telling journalists they were there to stay and would get services up and running again.

Since fighting escalated last week, electricity and water supplies in the city have been cut off, and food is scarce.

"We will continue the march of liberation all the way to Kinshasa," Nangaa added.

Analysts say such an offensive would be unlikely given the vast size of the country - Kinshasa is 2,600km (1,600 miles) away. However, it did happen in 1997, when Rwanda-backed forces ousted long-time leader Mobutu Sese Seko.

Nangaa's comments will increase anger in Kinshasa, which has accused neighbouring Rwanda of backing the rebels, and even having its troops in Goma.

Rwanda is also facing a chorus of international criticism, despite its denials of direct military support.

M23 - the main rebel group in the alliance - is led by ethnic Tutsis, and says it took up arms to protect the rights of the minority group in DR Congo.

Rwanda's President Paul Kagame is also a Tutsi, and accuses DR Congo's government of harbouring Hutu militias who were involved in the 1994 genocide in Rwanda.

Both the UN and the southern African regional bloc Sadc have peacekeepers in the east, but they failed to halt the rebel assault.

Peacekeepers from several counties have been killed in the conflict, with South African troops suffering the highest casualties - 13.

On Wednesday, Kagame said Rwanda was ready for a confrontation with South Africa if necessary, following a claim by President Cyril Ramaphosa that M23 fighters and Rwandan forces were responsible for the deaths.

In a strongly worded statement on X, Kagame accused Ramaphosa of distorting their private conversations.

"If South Africa wants to contribute to peaceful solutions, that is well and good, but South Africa is in no position to take on the role of a peacemaker or mediator. And if South Africa prefers confrontation, Rwanda will deal with the matter in that context any day," he said.

The exchange marks a significant escalation in tensions between the two nations, whose relationship has been fragile for several years.

Southern African leaders are due to hold a summit on Friday, with Kagame saying their regional force was "not a peacekeeping force, and it has no place in this situation".

In contrast, Tshisekedi paid tribute to the killed Sadc soldiers "fighting alongside us", as well as UN peacekeepers.

The UN, the European Union and countries including the US and China have all called on Rwandan forces to leave DR Congo.

The UK and Germany are among donor countries that have threatened to withdraw their aid to Rwanda in the wake of the M23 offensive.

UK Foreign Secretary David Lammy said on Wednesday that £32m ($40m) of annual bilateral aid was under threat, while Germany has cancelled aid talks with the country.

Additional reporting by Nomsa Maseko in Johannesburg