By Gustavo Palencia

TEGUCIGALPA (Reuters) - Honduras ordered 1,000 military police onto the streets of its most violent cities on Monday, as a presidential election dominated by debate over how to tackle the wave of drug killings approaches in just over a month.

This first deployment of a new military-style police force marks the latest tactic to curb an epidemic of drug violence that last year turned Honduras into the world's most murderous country with more than 85 homicides for every 100,000 people.

The Central American country has become a key staging point for drug shipments moving north from South America, and has been invaded by Mexican drug gangs.

In August, Congress authorized the creation the new force made up of 5,000 officers with military training. At the start of the year, the government had put 4,000 soldiers on the streets, but they have failed to end the killing.

"The operations of the military police, especially in the residential areas, will continue until we succeed," said army spokesman Colonel Jeremias Arevalo. "We're going to clean these areas from crime."

The security issue has become the focus of campaigning ahead of next month's presidential election that pits Xiomara Castro, the wife of former President Manuel Zelaya, against National Party candidate Juan Hernandez.

Castro, the Liberty and Refoundation Party candidate who established her reputation while fighting for her husband's right to rule after his 2009 military-led ouster, is slightly ahead of Hernandez according to the latest polls, but the lead is so small that statistically they are tied.

Castro and her party, a coalition of leftist politicians, unions, agrarian and indigenous groups, say they would create a community police force to tackle the violence, while Hernandez wants the military police force working alongside the army.

The winner of the election will take office in January 2014.

(Writing by Lomi Kriel and Gabriel Stargardter; Editing by Simon Gardner and Jackie Frank)