South Africa and Rwanda's already fraught diplomatic relations have worsened after President Cyril Ramaphosa accused the Rwanda-backed M23 rebel group of killing South African peacekeepers in eastern Democratic Republic of Congo.

As the rebels gained the upper hand in the battlefield by capturing most of Goma - the biggest city in the east - South Africa fired a diplomatic salvo, warning that further attacks on its troops would be considered a "declaration of war".

Rwanda's President Paul Kagame hit back, accusing South Africa of being part of a "belligerent force" involved in "offensive combat operations" to help the Congolese government "fight against its own people".

A total of 13 South African soldiers have been killed in the fighting since last week as the rebels made a lightning advance towards Goma - a major trading hub on the border with Rwanda.

Last year, another seven South Africans were killed in eastern DR Congo - making it one of the country's deadliest combat-related tragedies in recent times.

South Africa and Rwanda have long had a difficult relationship.

In 2014, South Africa expelled three Rwandan diplomats after an attack on the home of an exiled Rwandan dissident in Johannesburg.

Kagame's government responded by expelling six South African envoys.

Tensions seemingly eased after Ramaphosa's visit to Rwanda last year for commemorations to mark the 30th anniversary of the genocide in which about 800,000 people were killed.

But they have flared up again, following the death of the South Africans who were deployed to eastern DR Congo in December 2023 as part of a regional peace-keeping force sent by the Southern African Development Community (Sadc)

South African soldiers make up the bulk of the force - known by the acronym SAMIDRC - that had the mission of repelling armed groups such as the M23 and bringing peace to the mineral-rich region following decades of unrest.

The latest diplomatic fall-out started with a post shared on Ramaphosa's X page.

In it, the president confirmed he had spoken to Kagame about the escalating conflict and that both leaders had agreed "on the urgent need for a ceasefire and the resumption of peace talks by all parties to the conflict".

Ramaphosa also insisted, in a later statement, that the presence of South African troops in DR Congo was not a "declaration of war against any country or state" - an apparent reference to Rwanda.

South Africa's Defence Minister Angie Motshekga, however, had a slightly different take, telling reporters: "There's been no hostilities between us, it's just that when they were firing above our heads, the president did warn them [that] if you're going to fire, we're going to take that as a declaration of war."

But Ramaphosa went further on X, saying the peacekeepers were killed in attacks by the M23 and - he pointedly added - "Rwanda Defence Force (RDF) militia".

This angered Kagame, who said statements made by South African officials - including Ramaphosa - contained lies and distortion.

"The Rwanda Defence Force is an army, not a militia," Kagame replied on X.

"President Ramaphosa has never given a 'warning' of any kind, unless it was delivered in his local language which I do not understand. He did ask for support to ensure the South African force has adequate electricity, food and water, which we shall help communicate.

"President Ramaphosa confirmed to me that M23 did not kill the soldiers from South Africa, [the Conglese army] FARDC did," Kagame said.

He added that the regional peacekeepers - who included troops from Tanzania and Malawi - were a "belligerent force" working alongside "genocidal armed groups" that targeted Rwanda, and had "no place in this situation".

Kagame closed his lengthy statement by saying South Africa was in "no position to take on the role of a peacemaker or mediator" and if the country wanted a confrontation, Rwanda would "deal with the matter in that context any day".

Kagame's comments clearly suggested that he wants South Africa to back off from DR Congo, where its military involvement dates back to the late 1990s.

It first joined the UN's peacekeeping mission, Monusco, following the end of the racist system of apartheid in 1994.

At the time, the South Africa's military had just emerged from being regarded as a "highly effective apartheid war-time force" to a "peacetime force" left to grapple with reduced funding and a "lack of political direction", Thomas Mandrup, an associate professor at the country's Stellenbosch University, told the BBC.

While South Africa has said its involvement in DR Congo was guided by its need to "contribute to the stability" of a fellow Sadc member, defence analyst Dean Wingrin said the country's economic interests also influenced its decision.

"The DRC is a very big trading partner with [us] because eastern DRC is so rich in minerals. We import a lot of minerals… from the DRC so South Africa has an interest in a peaceful DRC," he told the BBC.

While Monusco's mission has largely been about peacekeeping, escalating tensions in the region led to the establishment of the Force Intervention Brigade in 2013 to "actively engage" with the numerous armed groups in eastern DR Congo.

This intervention had initial success in repelling the M23, the most prominent rebel group.

This was partly due to the deployment of South Africa's attack aircraft - Rooivalk - which had a "devastating effect" on the M23 in a short space of time, according to Mr Wingrin.

The rebel group then effectively melted away and was subsequently expelled from eastern DR Congo - until its recent comeback which has seen it capture much of the region.

However, South Africa's military has been in no position, this time around, to thwart the rebel group's advance as it has lost its airpower.

"Unfortunately South Africa's budget has continued to decline over the years. The air force couldn't afford to maintain the Rooivalks," Mr Wingrin said.

"We're missing that vital aircover that would've come in so handy a few days ago but is way too late now," he said.

Mr Mandrup expressed a similar view, saying South Africa deployed its troops in 2023, ignoring warnings that "you haven't got the capabilities needed, the defence force is in shambles and you're facing an opponent that's much better equipped than in 2013".

He added that it was difficult for South Africa to bring back its troops at this point because the "forces are locked down and caught in two bases".

"They can't get out, get aircover [or] reinforcements. They can't even get the wounded out," he said.

Ramaphosa seemed to agree, saying in a recent statement that the situation in the region was "tense, volatile and unpredictable".

In spite of this, any decision to pull South African troops out of DR Congo ultimately lies with Sadc since SAMIDRC was deployed by the 16-member regional bloc.

There are reports that Sadc is set to take this decision at a summit taking place on Friday.

For Mr Wingrin, there was a need for the South African government to do "serious introspection" over its military involvement in DR Congo.

"Is it something they want to push at all costs and what is it worth to South Africa to have sons and daughters dying so far away?" he asked.

So, South Africa's president appears to have a difficult choice – keep his soldiers in DR Congo and risk further deaths, or the embarrassment of pulling them out, presumably after negotiating safe passage for them with Rwanda.