By Jeremy Clarke NAIROBI, May 19 (Reuters) - Three Kenyan rangers and four poachers died during an overnight shootout in the remote south-east, the Kenyan Wildlife Service (KWS) said on Saturday. It was the latest clash in a decades-old war in the east African nation between wildlife rangers and poachers who kill big game like rhinos and elephants prized for their horns and tusks. "The Kenya Wildlife Service regrets to announce the death of three rangers who have been gunned down by bandits during an operation in Tana River District," the wildlife authority said of the clash in the early hours of Saturday. "During the fierce exchange of fire, the rangers killed four poachers while others escaped with injuries," it said, adding that two AK-47 rifles and two axes were seized. The rangers were part of a seven-member force patrolling the Idsowe area of Tana River district, some 350 km (215 miles) southeast of the capital Nairobi, KWS said. "During the same operation, one ranger corporal was also seriously injured and has been taken to Ngao Hospital in Tarasaa," it said. Poaching is a perennial problem in the east African country, whose wildlife parks are a major tourist attraction. Kenya is a focal point in Africa's booming illegal trade in animals and plants. The global trade is worth more than $10 billion each year, experts say, making it the world's third biggest source of criminal income after drugs and guns. KWS said an "intensive hunt" was underway for the poachers who escaped after Saturday's incident.