The opposition said its demand for free elections have not been met.
Separately, UN human rights chief Zeid Raad al-Hussein warned that a government-allied youth group was becoming increasingly violent.
Burundi has been hit by unrest and a failed coup since President Pierre Nkurunziza announced in April that he would run for a third term.
Western donors have cut some aid to the country, and say they will not help finance the election.
Mr Nkurunziza’s spokesman Philippe Nzobonariba said his decision to stand for re-election was “non-negotiable”, and the polls would not be delayed again.
Mr al-Hussein said his office received nearly 50 phone calls a day from people across Burundi pleading for protection.
The Imbonerakure youth group was accused of summary executions, tortures and beatings, and “could tip an already extremely tense situation over the edge,” he said..
The electoral commission proposed on Monday that presidential elections, originally scheduled for 26 June, take place on 15 July, which falls short of a call by regional leaders to delay the poll by at least six weeks.
The commission has suggested that parliamentary elections, originally due on 5 June, be shifted to 26 June.
None of the opposition parties attended the meeting where the commission unveiled the new dates, Reuters news agency reports.
A group of 17 opposition parties had earlier issued a statement saying they were committed to dialogue, but repeated their demand for the 51-year-old president, who survived a coup attempt last month, to quit, it reports.
The BBC French Service’s Venuste Nshimiyimana reports that one of the main opposition parties, the National Liberation Forces (FNL), has condemned the electoral commission’s proposal as unconstitutional.
FNL secretary-general Adolphe Banyikwa said the five-member body lacked a quorum, after two of its members fled to Rwanda because they feared for their lives.
Its decisions were, therefore, invalid, Mr Banyikwa said.
More than 20 people have been killed since 25 April in protests against Mr Nkurunziza’s bid to extend his 10-year rule.
More than 100,000 have fled to neighbouring states, aid agencies say.
Another opposition leader, Charles Nditije, told an international news agency d not hold elections in the current climate.
“If things remain as they are, we consider that it will be a masquerade, a parody of elections,” Mr Nditije is quoted as saying.
Meanwhile, the main civil society group in Burundi said it had written to UN chief Ban Ki-moon, demanding the resignation of his chief mediator, Said Djinnit.
Mr Djinnit had not focused on Mr Nkurunziza bid for re-election, which is the root of the crisis in Burundi, the letter said.
The opposition says Mr Nkurunziza’s attempt to run for office again contravenes the constitution, which states a president can only serve two terms.
But Mr Nkurunziza’s supporters argue that he is entitled to another term because he was first elected by parliament in 2005 – not voters. The Constitutional Court has ruled in favour of the president.