He later released seven hostages in exchange for permitting several reporters to enter the building, local TV stations reported.
However several police officers who had disguised themselves in the group overcame and arrested Paz in dramatic scenes shown on Colombian television.
No-one was reported injured in the incident.
Asylum request
The man, who identified himself to local media as Edgar Paz Morales, a former military official, asked for the media be brought to the scene.
He also demanded a meeting with Mexico's ambassador to Colombia, so that he could request asylum, AFP reported.
Local television images earlier showed him clutching a hand grenade in front of a group of hostages sitting in chairs.
He told local television channel City TV that the army was denying him a pension after 21 years of military service.
"I am a man who has fought for my country, but now it doesn't even acknowledge me," he also told Colombian radio.