Uganda's leading role in the inter-Burundi dialogue has come under scrutiny after the second round of talks failed to take off in Arusha last week.
The parties claimed that they were not informed of the exact date for the Arusha meeting.
Coupled with Tanzania's parallel shuttle diplomacy to salvage the talks that were set for January 6, the United States has cast doubts on Uganda's ability to broker a deal since President Museveni is also a beneficiary of extended term limits just like his Burundian counterpart Pierre Nkurunziza.
Uganda changed the Constitution in 2005 and Rwanda did the same last year albeit with popular support from the citizens to remove presidential term limits.
Launching the talks in Entebbe last month, President Museveni has asked warring parties in Burundi to end the violence and warned that he will investigate the killings of civilians in Bujumbura.
Tanzania is also keen on forestalling the crisis in Burundi, which has already left it and Rwanda hosting thousands of Burundian refugees.
Dar es Salaam is also said to be unsure whether the African Union's decision to deploy 5,000 troops in Burundi is appropriate before a local peacemaking initiative -- The National Inter-Burundian dialogue Commission (CNDI) -- is given a chance.
Sources within the African Union in Addis Ababa told The EastAfrican that the United States is not happy with President Museveni, who was selected by the EAC, continuing as the mediator.
The spokesman for the Burundi ruling CNDD-FDD, Daniel Gelase Ndabirabe, said Uganda faces a moral challenge in presenting an appropriate model of democracy for Burundi without the input from CNDI.
Dr Yolande Bouka, a senior researcher with the Institute for Security Studies in charge of the Great Lakes and Central Africa, said strong leadership, whether from Tanzania or Uganda, was needed to resolve the dispute.
"The future of the mediation and the management of the crisis would be better served with AU leadership alongside those in the EAC who are committed to peace," said Dr Bouka.
Last month, US Assistant Secretary of State for African Affairs Linda Thomas-Greenfield told the US Senate that political tensions within the EAC were impeding mediation, suggesting that the African Union should take over.
However, Uganda's Prime Minister Ruhakana Rugunda told the press early in the week that the talks would not be rushed until a consensus was built across parties Tanzania's Minister for EAC, Regional and International Relations Augustine Philip Mahiga, travelled to Pretoria on Wednesday last week to meet with the AU Commission Chairperson Nkosazana Dlamini-Zuma, seeking assurances that the AU would not necessarily deploy troops if the talks bore fruit.
Mr Mahiga also met President Museveni last week asking him to expedite the dialogue, which is being handled by Defence Minister Crispus Kiyonga.
Tanzania, the sitting EAC chair, has borne the brunt of Burundi refugees since the instability began in April last year with the current numbers standing at 122,839.
Nyarugusu camp alone in North West Tanzania, holds more than 100,000 Burundian refugees in addition to the existing 60,000 refugees from the Democratic Republic of Congo.
Willy Nyamitwe, Burundi's presidential spokesperson had prior to January 6 announced that the government would not attend the talks because the agenda was not clear and that some of the participants from the opposition side were involved in the May coup attempt.
Later in the week, Mr Nyamitwe said the talks in Entebbe on December 28 did not reach a consensus on the specific date of resumption of the dialogue.
"We were not aware of the dialogue that was set on January 6 because we never even received the invitation. The government position remains the same. We are concerned how the representatives of the opposition, civil society organisations and women representatives were invited to Entebbe," said Burundi Foreign Affairs Minister Alain Nyamitwe in an interview with The EastAfrican in Bujumbura.
The National Council for the Restoration of Arusha Agreement and Rule of Law (CNARED) spokesman Pancrace Cimpaye, also said his delegation had not received an invitation or given a tentative date.
Mr Mahiga convened a consultative meeting in Arusha on January 6 after the talks failed to takeoff to deliberate on the way forward.
The meeting attended by Dr Kiyonga, Dr Richard Sezibera, EAC Secretary General among others, committed to intensify consultations with the Burundi government and opposition to have the talks resume as soon as possible.The AU Peace and Security Council had in December resolved to send 5,000 African troops to Burundi to stop the killings and the violation of human-rights. But President Nkurunziza has stated that it would amount to foreign invasion and warned the country will fight AU forces if deployed.
This left AU with the only option of invoking Article 4 (h) of the Constitutive Act, which gives the continental body the right to intervene in a member state in respect of grave circumstances such as war crimes, genocide and crimes against humanity.
But this article can only be invoked with the approval of the heads of state, which means the issue will be referred to the heads of state summit in Addis Ababa later this month.
Sources at the AU Peace and Security Council say the objective of the force will be to consolidate peace and not attack the government.
Dr Bouka argues that the possibility of such deployment remains in doubt despite the Burundian government continuing to test the limits of the international community and regional partners.
"It is not surprising that after a ceremonial opening of the talks, the government delays the resumption of the process for the genuine negotiations to take place. It did the same things shortly before the presidential elections. This refusal to resume the talks in Arusha indicates that the government is still not committed to dialogue," she said.
Additional reporting by Havyarimana Moses