Representatives of Burundi's government and the opposition have started discussing peace negotiations in Uganda on Monday to end the political violence in Burundi.
Ugandan Defence Minister Chrispus Kiyonga is mediating the peace talks under the leadership of a regional unity which calls itself the East African Community.
"I really appeal to you, the two sides, to sit down and have a political solution so that you save the people from the suffering," Museveni said as the talks opened.
"You have no excuse not to sit down and quickly resolve... these are clear things, you can meet one afternoon and agree," he said.
Burundi has been in a cycle of deadly violence since President Pierre Nkurunziza’s victory in a disputed election following his decision to seek a third term despite a constitutional two-term limit.
Violence erupted across Burundi against Nkurunziza’s third-term bid and his disputed election victory last July.
The government's opponents and supporters have targeted each other with gun, grenade and rocket attacks.
At least 400 people have been killed and about 3,500 have been arrested in Burundi since April, according to the United Nations, including Burundian opposition figures and supporters - as well as a former army chief and a former intelligence chief - under a government crackdown.
According to the latest UN figures, more than 239,000 people have fled to neighbouring countries, fearing a possible genocide. Up to 55 percent of the refugees are under the age of 18.
There was a civil war in Burundi from 1993 to 2005 and approximately 300,000 people died in the conflict between rebels from the country's majority Hutu population and an army dominated by the Tutsi minority.