It said the two sides agreed to immediately put an end to their differences and end all armed presence on the street.
Some supporters of the Shia movement Amal were reportedly siding with Shia Hezbollah loyalists in the fight but the party later issued a statement denying that claim.
A security source said one of those killed was a local Hezbollah official.
"One of them is Mohammad Fawaz who is in charge of Burj Abi Haidar sector," he said.
Other security sources confirmed that Fawaz was killed. One source said an al-Ahbash supporter had also been killed.
Witnesses said the clash began as an argument between Fawaz and supporters of the Sunni group over a parking space near a mosque frequented by al-Ahbash.
Al Jazeera's Rula Amin, reporting from Beirut, said the clashes had "caught everyone by surprise" because al-Ahbash has been an ally of Hezbollah and Amal in the past few years.
"[Al-Ahbash] is a small, conservative Sunni group. Politically they've been allies of Hezbollah. They're very close to the Syrian government."
A security source told Reuters news agency that two people had been taken to hospital along with the Hezbollah official who later died from his injuries.
"When the news came out that the wounded Hezbollah supporter died in hospital, people went to the streets and now there is a lot of tension," the source said.
Witnesses said armed men could be seen standing on the corners and peering down alleyways in the neighbourhood, while families ran for cover.