The rebels shelled northern areas of Bujumbura overnight and a military spokesman said at least three people had been injured.
The refugees are sheltering in makeshift camps beside medical centres and religious missions.
UN Secretary-General Kofi Annan has called for unrestricted access to the refugees and expressed his dismay over the latest clashes - the worst in Burundi for several years.
He said Mr Annan stressed the need for the UN agencies to have full and unfettered access to the affected populations.
The fighting, which is now in its sixth day, is concentrated around the capital Bujumbura and is believed to have claimed around 40 lives.
Peace summit
A BBC correspondent who managed to get into the northern Kinama district - the scene of the fiercest clashes - said he was told by local residents that the Hutu rebels were in control.
The rebels shelled northern areas of Bujumbura overnight and a military spokesman said at least three people had been injured.
The rebels said they were launching mortar bombs on military targets in Bujumbura and would widen the scope of their attacks.
"We are not going to stay just in [the poor Hutu suburb of] Kinama. Our aim is the whole country," a senior rebel commander told Reuters new agency.
"We are aiming only at military targets, but unfortunately there often are civilian houses nearby that can be damaged."
Fighting had eased on Thursday, with just occasional mortar fire being heard.
The army said on Wednesday it had repulsed a rebel attack on Bujumbura and retaken control of suburban areas previously held by rebels.
The start of the latest fighting coincided with a peace summit chaired by Nelson Mandela in Arusha in Tanzania, where little progress appears to be made.
In any case, the rebel groups behind the offensive have not signed up to the peace process.
Burundi's civil war began after the assassination of the country's Hutu president seven-and-a-half years ago.
As many as 200,000 people are believed to have lost their lives in the conflict so far.