The original ceasefire, which was put in place in August, was nullified when the peace accord was rejected in plebiscite earlier this month. He had already extended it to October 31.
The decision comes as Santos and his team hear proposals from representatives of those who voted against the accord - rejected by a razor-thin margin of less than half a percentage point - as too lenient on the Marxist rebels.
Santos said he decided to extend the ceasefire further after meeting with student leaders who had organized two huge marches through Bogota to show support for a peace accord, Reuters reported.
The ceasefire can be extended further, but Santos said he hopes a new deal is approved long before then.
Santos won the 2016 Nobel Peace Prize on Friday for his efforts to end the war.