A vote cannot be held for another week under parliament rules, and Marape has said he is confident he has the numbers to defeat the motion.
The largest Pacific Island nation, PNG struck a defence co-operation agreement with the United States in May and is also being courted for security ties by trading partner China.
In his first comments to parliament on the riots, Marape was critical of police for taking strike action over a salary error, and said a judge would be appointed to hold a commission of inquiry into conduct of the police force on January 10.
During the 10 hours police were not on duty in the capital Port Moresby, allowing rioters to cause "mayhem", citizens had defended their suburbs and businesses, Marape said on Tuesday.
Sixteen people were killed in the rioting.
"We will not allow ill-discipline in our police force," he said.
The defence force was not involved in the riot, Marape said, revealing that a military commander had asked to assist when Marape's office came under attack from rioters.
"I said you will not bring your soldiers in," he told parliament.
On a visit to Australia last week, Marape sought progress on a security and policing agreement struck in December that will see Canberra provide $A200 million to boost police training and recruitment.
