Africana55 Radio 
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Tshisekedi's second term ends in 2028 but in May he said that elections, which are due then, may not be held because of the conflict.
He also hinted that he may seek re-election for a third term "if the people want".
The parliament has since passed a bill that could pave the way for a referendum that could remove the constitution's two-term limit.
Last month, authorities clashed with protesters holding demonstrations in the capital against the proposed changes.
Richard Moncrieff, who monitors Africa's Great Lakes region for the International Crisis Group (ICG) says the new coalition is aimed at trying to enlarge the rebellion.
He argues that through his "higher profile", Kabila hopes to get support from people dissatisfied with Tshisekedi "beyond the very narrow political base that the M23 enjoys".
The analyst says this appears to be Kabila's objective, to draw more senior Congolese army officers to his side and "lessen the reliance of the M23 on its Rwandan backers".
Kabila came to power after the assassination of his father Laurent Kabila, who headed a national rebellion in the 1990s, backed by Rwanda. His forces marched across the country, starting in the east, before taking over in the capital Kinshasa, some 1,500km (1,000 miles) away.
Moncrieff says Kabila is drawing on that past to proclaim the illegitimacy of Tshisekedi's government.
He however says it won't be easy to seize power like his father, partly because the US has imposed sanctions on Kabila, which he says presumes American support for DR Congo's government.
In May the US imposed sweeping sanctions on Kabila, accusing him of backing the M23, providing financial support, encouraging defections from the Congolese army. Kabila said the measures were unjustified and politically motivated.
The US said they were part of a wider effort to support last year's peace deal between DR Congo and Rwanda that it brokered.
The latest events show peace negotiations are "going nowhere and attempting to gain control on the ground is the priority for all parties," the ICG analyst says.