Leading Burundian dissident Hussein Radjabu has told the BBC that he escaped from prison last week by walking "upright... under the beam of floodlights without any problem".
Burundian police have said prison officials aided the escape.
Radjabu said he was now with his supporters - but did not specify where.
The governing party's ex-chief was seen as Burundi's most powerful man until his arrest in 2007, amid a rumoured rift with President Pierre Nkurunziza.
In his interview with the BBC, Radjabu accused the president of having orchestrated his dismissal as party chief, as well as a subsequent trial on charges of plotting against the state.
Radjabu's escape came eight years into his 13-year prison sentence. He said plans had been afoot to harm him since he was sent to prison. He escaped because it was "the right time for us to do so".
Tension has been growing in Burundi over the president's apparent plans to seek a third term. The move is barred by the constitution and by the Arusha peace deal of 2000, which ended a seven-year civil war.
The governing CNDD-FDD party is said to be split between those who support Mr Nkurunziza's intention to stay in office, and those who oppose it.
Radjabu rejected the coming elections as a sham. He told the BBC he was still the chair of the governing party and that President Nkurunziza should recognise this.
A Burundi police spokesman told the AFP news agency last week that Radjabu's escape had been aided by at least three guards, including the chief warden in charge of the prison's security.
At least two other inmates escaped with him into vehicles that had been waiting outside the prison, the spokesman said.
The escape reportedly took place before midnight on Sunday evening, at a time when many guards were asleep.
In 2005, Mr Nkurunziza, a former Hutu rebel leader, became the first president to be chosen in democratic elections since the start of Burundi's civil war in 1994.
Radjabu, who was also a rebel leader, became the head of the CNDD-FDD at the same time. He was regarded as the real power in the country.
Many Burundians saw his arrest in April 2007 as politically motivated.
Mr Nkurunziza was re-elected in June 2010. The vote was boycotted by the opposition, which complained of fraud in the earlier local elections.
Opposition leaders and international observers have since complained of a growing crackdown on opposition parties and the media.