MANILA — President Rodrigo Duterte of the Philippines on Thursday said for the first time that extrajudicial killings had happened under his government’s brutal war on drugs, an admission that could bolster two cases filed against him at the International Criminal Court.

In a rambling speech before government executives at the presidential palace, Mr. Duterte again touched on the government’s drug war that has left thousands dead, a common theme in his two-year-old presidency.

He said he had challenged the country’s military and police brass to remove him from office if they were not satisfied with the way he was running the country.

“I told the military, what is my fault? Did I steal even one peso?” Mr. Duterte said. “My only sin is the extrajudicial killings.”