The flare-up comes despite peace talks in Havana aimed at ending the 50-year-old insurgency and as the FARC denounced the killing of leftist activists.
The military source said today's fighting was in the central department of Meta where an army operation resulted in the deaths of five guerrillas and the capture of eight others.
Yesterday, the army reported seven guerrillas killed in a separate operation in the department of Tolima, also in the central part of the country.
Colombian President Juan Manuel Santos has vowed to keep the pressure on the FARC even as his government pursues peace talks with the group in Havana.
"The offensive continues," he said today during an official visit to Spain.
"But at the same time we seek to negotiate so that all this violence, which has bloodied the country for 50 years, will be set aside and we can continue to grow without violence," he added.
"What concerns me is that they might commit an irrational act, an attack against a very important person, something that would shatter the process into a thousand pieces," he said.
In Havana, meanwhile, the chief FARC negotiator Ivan Marquez charged that 29 members of Marcha Patriotica, a leftist group aligned with the FARC, have been murdered over the past two years.
"We cannot tolerate in the midst of a peace process that the Marcha Patriotica is systematically destroyed, day by day," said Marquez.
The talks began in November 2012, and so far have worked out preliminary agreements on two of five agenda issues.