The high-ranking member of the Venezuelan government asked to remain anonymous. CNN has not been able to independently confirm Perez's death.
But, in a Monday speech to lawmakers, President Nicolas Maduro described an operation to hunt down the "terrorist group that attacked the Supreme Court." Maduro said the targeted group was preparing a car bomb attack against the embassy of an unnamed country.
As a result of the operation, part of the terrorist group "fell down" and five people were arrested, he said, without detailing how many died or who they were. Two officers were killed in the siege, he said.
"Everyone who embarks on the path of terrorism and takes up arms against the republic -- against the people -- will get their response in due time from our armed forces and from our police forces. They should not doubt that," he said.
According to a statement from the country's Interior Ministry, heavily armed men from a "terrorist cell" opened fire on police and attempted to detonate a vehicle full of explosives, state broadcaster VTV reported.
The Interior Ministry said two officers were killed and five injured, and five people from the "terrorist cell" were arrested, VTV reported. Authorities have not released the names of those killed or captured.
The encounter took place in the western Caracas neighborhood of El Junquito.
Earlier Monday, Perez posted videos on social media saying his group was under attack. In the video, Perez holds a rifle and speaks to the camera with what appears to be blood on his face.
"We are not shooting and they keep attacking us," Perez says. "We are trying to negotiate because there are innocent people here, there are civilians ... they literally want to kill us."
Perez, an officer in the country's investigative police force, is known for leading a helicopter attack against the Ministry of Justice and the Supreme Court in June. The helicopter circled the city as Perez and his group, Equilibrio Nacional (National Balance), attacked the buildings with grenades and gunfire. No one was injured.
Perez disappeared after the incident and was declared a fugitive by President Nicolas Maduro's government.
"It is better to go out and fight for a new future than to die kneeling to this regime," Perez said