Mr Santos said the move was in recognition of the fact a unilateral ceasefire declared by Farc was holding.
But operations against another guerrilla group – the National Liberation Army (ELN) – will continue.
Colombia’s government and the Farc are holding peace talks in Cuba.
“In regards to the indefinite, unilateral ceasefire declared by the Farc on December 18, we must recognize that they have fulfilled it,” Mr Santos said in a televised address.
“In order to start the de-escalation of the conflict, I have decided to order the minister of defence and armed forces commanders to stop bombing raids on Farc camps for a month,” he added.
Breathing space?
President Santos was critical of the smaller Colombian rebel movement, the ELN, saying the group had “increased its criminal activities”.
His conservative opponents say halting the bombing will give the rebels valuable breathing space. Aerial raids have been a key component in the government’s military campaign.
Farc negotiators have been engaged in peace talks with the Colombian government since November 2012.
They have reached partial agreements on a number of issues, including on the drugs trade, land reform and political participation, although they have yet to reach a final deal.
A peace commission composed of Colombian businesspeople and politicians is to be formed to help guide the process through its final stages, Mr Santos said in his speech.
Stumbling blocks
Farc, the largest of Colombia’s rebel groups, was founded in 1964 with the aim of installing a Marxist regime.
In the 1990s the group was forced to change tactics because of attacks from right-wing militias and became increasingly involved in the cocaine trade to raise money.
It has seen numbers drop from 16,000 to 8,000 in recent years, but rebels still control rural areas particularly in the south and the east.
Farc is listed as a terrorist organisation by the US and Europe.
At the weekend, the two sides announced plans to work together to clear unexploded landmines.
More than 220,000 people are estimated to have died in five decades of conflict.
By:BBC
