Monaco striker Radamel Falcao has been left off Colombia's squad for the World Cup after failing to recover from a knee injury.

Colombia coach Jose Pekerman made the announcement Monday from the team's training facility in Buenos Aires, Argentina, dealing a serious blow to the team's chances at the tournament.

Colombia was a favourite to win Group C, which includes Japan, Greece and Ivory Coast.

Falcao's presence had been in doubt ever since he underwent knee surgery in January. But Colombians had been hoping for a miracle recovery in time for the World Cup as Falcao posted on social inspirational messages and photos of himself taking nine-kilometre runs.

"We can say to all of Colombia that he did more than was within his power to play," Pekerman said. "He deserved the right for us to wait and keep the hope alive."

"I had great hope to play," Falcao said. "But, well, one has to support the team from outside and wish it the best." 

The 28-year-old said that as he lacked match fitness, "the smartest thing to do" is to stay on the sidelines. He said he still plans to travel to Brazil to cheer on his teammates.

Falcao's nine goals in the South American qualifiers paved the way for Colombia's return to the World Cup for the first time since 1998. It opens against Greece at Belo Horizonte on June 14.