Randy Hultgren asked Trump to highlight the human rights situation in the Philippines in his upcoming visit to Manila for the 31st Association of Southeast Asian Nations Summit.
Duterte's spokesman Harry Roque told CNN affiliate CNN Philippines in a text: "I think it was in jest".
In other photos, Duterte was seen shaking hands with Mexican President Enrique Peña Nieto and South Korean president Moon Jae-in.
"That's because the US President is flying to the Philippines for the ASEAN Summit tomorrow", he added.
"There's a photo posted by the Special Assistant to the President Bong Go".
Duterte was able to meet and talk with top world leaders on the sidelines of the APEC summit.
Mr Trump, who has said Mr Duterte is doing "a great job", himself came under criticism during his 2016 presidential run, when he told a campaign rally in Iowa: "I could stand in the middle of Fifth Avenue and shoot somebody and I wouldn't lose any voters, OK?"
"Duterte's Haell", a Field of Vision documentary on the Philippine president's drug war, directed by Aaron Goodman and Luis Liwanag.
Roque reiterated that Duterte "will refuse to pursue any talks relating to a domestic issue such as on his war on drugs".
Philippine President Rodrigo Duterte, whose bloody war on drugs has led to the deaths of more than 12,000 Filipinos, boasted on Thursday that he is no more concerned with killing now than he was at the age of 16, when he said he stabbed a man to death just because he looked at him the wrong way.
In September, the Duterte-controlled Philippines lower house voted to allocate a budget of less than US$20 to the independent body, a decision Callamard described as "reprehensible and unconscionable".
"The position is: The use of force by state agents, of course, is not absolutely prohibited".
On October 30, Duterte said he would raise the issue on the escalating tension between the U.S. and North Korea over the Korean peninsula.
Shortly after those remarks, Duterte proposed hosting an worldwide human rights summit in the Philippines, saying countries like the U.S., France and Russian Federation needed to be investigated for violating human rights. "He wants to emphasize that as a public prosecutor for 10 years, it is not his intention to violate and commit murders - to violate human rights and to commit murders", he added.
The President is expected to be back in Manila before 11 p.m. Saturday.