By Hugh Bronstein BOGOTA, Jan 15 (Reuters) - Leftist Colombian rebels killed 11 soldiers and police over the weekend, showing their cocaine-fueled insurgency is far from over and prompting analysts to question the country's U.S.-backed military strategy. Colombia has received about $4 billion in U.S. aid since 2000 aimed largely at fighting the 17,000-member Revolutionary Armed Forces of Colombia, or FARC, which uses the cocaine trade to fund its 42-year-old war against the state. Six soldiers were killed on Saturday by mines planted by the FARC in eastern Colombia near Venezuela. On Sunday a police truck was hit with a homemade mortar on the other side of the country near the town of Puerto Asis in Putumayo province, a focal point of the "Plan Colombia" anti-drug program. "If the FARC can still do this in an urban area that has been the center of the anti-drug fight, it opens serious questions in Washington and in Bogota," said Pablo Casas, an analyst with Bogota think tank Security and Democracy. The incident, in which five police were killed, happened near the Ecuadorean border, where Colombia sprays herbicides on coca crops used to make cocaine. Ecuador has complained that the fumigation threatened health and agriculture on Ecuador's side. Popular for cutting urban crime and making the highways safer as part of his crackdown on the FARC, Colombian President Alvaro Uribe won re-election by a landslide last year. But the guerrillas still govern wide rural areas. "Some things have gotten better in Colombia but, as the Putumayo attack shows, the fundamental threat posed by the FARC remains. This suggests there needs to be a rethinking of strategy," said Michael Shifter, an analyst at Washington-based Inter-American Dialogue. "The Colombian state needs to maintain not only a military presence in these areas but a presence in terms of health, education and other services that show local populations that there is an alternative to the FARC," Shifter added. Uribe, whose father was killed by the FARC in the 1980s, is a key U.S. ally in the Andean region. Leftist Rafael Correa was sworn in as Ecuador's president on Monday and anti-U.S. firebrand Hugo Chavez of Venezuela shocked the markets last week by saying he will nationalize power utilities in a move to reinforce his socialist revolution.