During a visit to Baghdad, Mr Tugendhat said British officials “want to build on our strong counter-terrorism co-operation" and expand the countries' security relationship to “identify and address shared serious organised-crime threats.”
“Human smuggling, trafficking, narcotics and money laundering that work together as a criminal network that undermines the entire state of Iraq," he said.
In recent years, Iraq has primarily served as a transit country for drugs – particularly the amphetamine Captagon, which is largely produced in neighbouring Syria.
But there have been indications that production was also moving into Iraq.
Mr Tugendhat said Iraqi authorities discovered last month a factory that was producing Captagon in a province bordering Saudi Arabia, for easier entry to the kingdom.
Captagon smuggling - in pictures
“There is always an overlap between drugs, human trafficking, terrorism and violence,” Mr Tugendhat told reporters.
"We are seeing criminal groups, human trafficking and drugs affecting not just Iraq, but the whole region and many of our friends and allies in the region.”
Iraqi Prime Minister Mohammed Shia Al Sudani said in a statement that his country has made “significant efforts” to battle drugs and human trafficking.
Mr Al Sudani said the Iraqi and British interior ministries were preparing to sign a agreements outlining their co-operation on these issues.
A British official said the agreements would focus on sharing information to support counter-terrorism and against “serious organised crime".