Mkapa (pictured), who is the facilitator of the Burundi peace talks, did not immediately give a new date for the resumption of negotiations.
“Following consultations between the facilitator in the Burundi dialogue … and East African Community (EAC) Secretary General Liberat Mfumukeko, the resumption of the dialogue which was due on May 2-6 has now been postponed,” said a statement issued by the facilitator's office.
The office said that the dialogue would now likely take place in the third week of May.
Earlier last week, the Burundian government said that it would not participate in the talks, arguing that it had not been consulted, and went ahead to give a set of conditions to be fulfilled beforehand.
Previous talks mediated by Uganda’s President Yoweri Museveni failed to make any headway.
Meanwhile, violence in the tiny east African country continues to escalate. The country is facing a year-long political crisis that broke out since April 2015 following the announcement by Burundian President Pierre Nkurunziza that he would be seeking a third term.
"I am disappointed by the postponement of the Burundi dialogue that was due to take place in Arusha ... under the guidance of former President Mkapa. I fully support the efforts of President Mkapa and his team and their goal of ensuring that this dialogue is for all Burundians," Britain's minister for Africa, James Duddridge, said in a statement.
"I am extremely concerned at the recent increase in killings in Burundi, including the recent assassination of Brigadier General Athanase Kararuza and the attempted assassination of the Minister of Human Rights, Social Affairs and Gender, Martin Nivyabandi."
Duddridge condemned the attacks and the ongoing human rights abuses in Burundi, including alleged torture and ill treatment by the security services.
"By refusing to engage in an inclusive dialogue, the government of Burundi is actively obstructing the national reconciliation process that will put an end to these crimes," he said.
International observers fear that the ongoing conflict in Burundi might escalate into an ethnic war between Tutsis and Hutus. The latest bloodshed comes as the International Criminal Court (ICC) has launched a probe into Burundi's year of violence.
Brig. Gen. Kararuza, a security adviser to Burundi's vice-president, was shot dead while dropping off his daughter at school.
Kararuza and his wife died instantly, while their daughter was injured. No group has said it was behind the attack in the capital, Bujumbura.
More than 400 people have been killed in unrest since President Nkurunziza said he would run for a third term last April.
A string of high-ranking army officials have been targeted during the conflict.
Security forces have also been accused of killing opponents and dumping them in mass graves by rights group Amnesty International.
Shortly after the attack in Bujumbura, the International Criminal Court announced that it was starting a preliminary investigation into the violence in Burundi.
This will decide whether a full-blown investigation will take place, which could result in charges against those accused of being behind the violence.