President Abelardo de la Espriella has lifted a decade-long suspension on permits to carry legal firearms.
CCTV footage later showed him climbing out unassisted and walking away, leaving his motorcycle behind.
It is a step towards ending a plan to stop violence by bringing rebel and criminal groups to the negotiating table.
Four members of an indigenous family are among the dead, witnesses said.
Following a 10-hour rescue operation, emergency workers pulled the 32-year-old from beneath slabs of concrete.
BBC Mundo has gone to the site of Torres del Limonar, a collapsed building in Cali where rescue workers fight to free survivors.
Most deaths from the magnitude-7.4 quake were reported in Cali, Colombia’s third-most populous city, as crews search collapsed buildings for those still trapped.
Colombia experienced a number of aftershocks on Tuesday, as efforts continued to free survivors trapped in rubble and buildings.
More than 900 people were injured in the quake, with more feared trapped under collapsed buildings.
