The authorities on Monday said a civilian was also shot dead by the army patrol.
The confusion just days before elections dealt a blow to Alvaro Uribe, the Colombian president, who has led a military crackdown on the Revolutionary Armed Forces of Colombia People's Army (Farc-EP) rebels, paramilitary militia and the cocaine trade that illegal armed groups use for financing.
Camilo Ospina, the defence minister, said: "In the course of army and police operations ... there was an incident involving the security forces during which 10 police and one civilian were killed."
The incident took place in a rural region of Valle province, where drug-traffickers and the 17,000-strong Farc, the country's largest Marxist rebel group, are active.
Uribe, a Washington ally whose government has received billions of dollars in US anti-drug and military aid, is popular for reducing crime and kidnapping in the cities and is expected to win re-election in Sunday's ballot.
But thousands of people are still killed or forced from their homes each year by illegal armed groups who control large parts of Colombia's rural countryside and jungle.
Uribe was elected in 2002 promising to smash the Farc insurgency. Since then, his government has demobilised 30,000 right-wing militia fighters and started talks with the smaller ELN rebel group. Farc will not negotiate.
Colombia's security forces have been involved in eight so-called friendly fire incidents since 2004 that have killed 32 soldiers or police officers and five civilians.