Mr Thaksin has launched the three-month campaign at police headquarters in Bangkok, asking authorities to focus on the country's bars and nightclubs in big cities.
Mr Thaksin's 2003 war on drugs left an estimated 2,894 people dead nationwide.
The killings were widely criticised by human right activists.
Police have insisted that only 72 people were killed by security forces, and that 1,329 of the deaths were related to drugs.
The second round of the war on drugs was in 2004, but authorities have not revealed how many people were killed during that crackdown.