Instead, the African Union is to send envoys for more talks, although previous negotiations have done nothing to end months of conflict.
The United Nations has warned that Burundi risks a repeat of the 1993-2006 civil war, with hundreds of people killed since April 2015, when President Pierre Nkurunziza announced he would stand for a controversial third term.
At least 230,000 people have fled to neighbouring countries.
Burundi has consistently opposed the idea of the AU's planned 5,000-strong peacekeeping mission, saying the deployment of troops without its express permission would be tantamount to an "invasion force".
But top AU diplomat Ibrahima Fall said today that sending troops without Burundi's approval was "unimaginable," with the bloc deciding to send envoys to hold talks with the government.
"There is no will neither to occupy nor to attack," AU Peace and Security Council chief Smail Chergui added, saying that troops could be sent in the future "if Burundi accepts it".
Clashes between government loyalists and the opposition have become increasingly violent.
Burundian Foreign Minster Alain Aime Nyamitwe told reporters he was "satisfied" at the decision and said Bujumbura was "open to cooperating with the international community, particularly the African Union."
But he also questioned why AU envoys would want to take the time to travel to Bujumbura "since "everyone is aware of the position of Burundi" already.
Chad's President Idriss Deby, speaking after he took over the post of African Union chairman yesterday, warned colleagues against inaction.
