The bodies and personal belongings of the 298 people who died when the Boeing 777 was shot down Thursday have been sitting in a debris field stretching roughly a mile in eastern Ukraine.
Malaysia Airlines on Saturday released a full passenger manifest indicating the majority of the victims -- 192 -- of the crash were from Netherlands.
Rutte said it was Netherlands' highest priority to reclaim the remains from the crash site.
"Anyone who fails to cooperate fully and immediately is leaving themselves open to very serious suspicions," he said.
"I am shocked by the images of completely disrespectful behavior at this tragic place," he added. "In defiance of all the rules of proper investigation, people have evidently been picking through the personal and recognizable belongings of the victims. This is appalling.
And it is undermining efforts to investigate and reconstruct what happened."
Rutte said Dutch forensics experts were on their way to the crash site and he called for full, unimpeded access for them.
"President Putin pledged his full cooperation regarding unhindered access to the crash site when we spoke on the phone yesterday. Following today's developments and the pictures we saw this morning, I sent a message in writing to the president urging him to exercise his influence on the militias," Rutte said.
"I told him that the window of opportunity to show the world that he intends to help is closing rapidly. He must take responsibility vis-à-vis the rebels and show the Netherlands and the world that he is doing what is expected of him. Yes, by exercising his influence," he added.