* President says violence shows cartels are weakening
* U.S. urges Monterrey staff to keep children at home (Adds Mexico's purchase of search drones)
MEXICO CITY, Aug 24 (Reuters) - Mexican President Felipe Calderon warned on Tuesday that more bloodshed will likely occur as his government continues its campaign to defeat violent drug cartels.
More than 28,000 people in Mexico have died in drug violence since Calderon launched his drug fight when he took office in late 2006, and gruesome attacks are on the rise.
Over the weekend, four decapitated bodies, their genitals and index fingers cut off, were hung upside down from a bridge in a popular getaway outside Mexico City. Another two bodies were dumped near the same bridge on Tuesday, police said.
But Calderon told a local radio station that escalating bloodshed was a sign that the cartels were on the run.
"I don't rule out that there might be more bouts of the violence we're witnessing, and what's more, the victory we are seeking and will gain is unthinkable without more violence," Calderon said. "This is a process of self-destruction for the criminals," he added.
Backed by millions of dollars in U.S. aid, Calderon has sent more than 45,000 troops and thousands of federal police to fight the cartels that are battling over smuggling routes into the United States and Mexico's growing local narcotics market.
Unmanned surveillance planes could be a new tool in finding secret drug fields since Mexico bought several unmanned drones earlier this year. [ID:nN24277050]
Full coverage of drugs war:
Factbox on political risks in Mexico [ID:nRISKMX]
Factbox on latest attacks [ID:nN23253814]
Despite taking down several top drug lords and making tens of thousands of arrests, Calderon faces pressure in Mexico as growing insecurity scares off some tourists and hurts local businesses extorted by drug gangs. Some foreign investors have put investment plans in border factories on hold.
Investment is crucial for Latin America's second largest economy as it recovers from its worst recession since 1932.
Calderon compared himself to a doctor who diagnosed cancer. "The cancer didn't start when the doctor arrived and detected it. It comes from way back," he said.
Most Mexicans support Calderon's drug war, but a jump in civilian deaths and the government's failure to stop violence spreading to cities like wealthy Monterrey near the U.S. state of Texas is prompting calls for a change in strategy.
After drug hitmen attacked private security guards outside an elite private school in Monterrey on Friday, the U.S. ambassador in Mexico urged U.S. consular staff in Monterrey to keep their children at home.
"The sharp increase in kidnapping incidents in the Monterrey area ... present a very high risk to the families of U.S. citizens who might be become incidental victims," the consulate said in a statement.
Drug trade analysts say the army alone cannot defeat the cartels and that Calderon risks serious lawlessness if he does not follow through with reforms to the justice, police and prison systems, where corruption is endemic. (Reporting by Robin Emmott; Editing by Missy Ryan and Stacey Joyce)