Investigators want the parents of missing 11-month-old Lisa Irwin to submit to separate interviews and answer a list of "tough questions" that detectives "need answered."
Kansas City Police Capt. Steve Young made his statement as the investigation into the toddler's disappearance entered its fourth week without any suspects or leads to the girl's whereabouts.
Police are still intent on interviewing the parents, Deborah Bradley, 25, and Jeremy Irwin, 29.
"We need them to sit down apart from each other, with detectives, and answer the tough questions detectives have for them concerning what they may or may not know about anything, who came and went [the night Lisa disappeared]," Young told ABCNews.com. "There's a whole list of things that they may know."
Young said he is "not disputing" family attorney Joe Tacopina's claims that the family has cooperated and answered other questions, such as specific questions regarding tips and leads. But that is not sufficient, he said.
"The bottom line is detectives need to sit down with them unrestricted and they need to answer questions that we need answered," he said.
Baby Lisa Cops Wants Parents to Answer "Tough" Questions
The captain rejected any suggestion that the case has hit a dead end.
"It would be far from reality to call this a cold case," Young said. "We're still looking at everything."
Young made his comments as Tacopina unleashed more criticism of the investigation, telling "Good Morning America" today that the parents have cooperated with numerous searches and interrogations.
"It really is maddening to me to listen to this police spokesperson come out there, and instead of informing the public—and more importantly the family—about leads and the status of the investigation and the manhunt, he comes out and makes these statements," Tacopina said. "And, quite frankly, they've [parents] done everything they've been asked to do...They have nothing to hide. They want answers."
When asked if there are restrictions on the conversations Lisa's parents will have, Tacopina said, "Oh, there's a restriction. I'm imposing that the questioning is going to be in good faith and fair and not the questioning that was done within an hour of baby Lisa's disappearance."
Tacopina claimed police accused Bradley of murdering her child within an hour of beginning to interrogate her.
"That's just not good investigatory tactics and it doesn't build good faith in them," Tacopina said.
He said Bradley would be willing to sit down for questioning "as long as the investigators doing the questioning are ones who have not previously determined guilt before having a stitch of evidence. We want a fair investigation."
Tacopina and another lawyer for the parents Cyndy Short have criticized the investigation in recent days.
Young declined to comment on Tacopina's remarks today other than to say, "I stand by all my previous statements."
Tacopina said the focus of the investigation should return to the three people who claim they saw a man carrying a baby dressed only in a diaper walking on the road in two different places on the night Lisa disappeared.
Baby Lisa Cops and Parents' Lawyers Clash
"That should raise all the red flags that it raises in my head to anyone who's out there really trying to do an investigation that includes a hunt for Lisa, and hopefully an alive and well Lisa," he said.
Mike Thompson, the witness who claims he saw a man carrying a baby on the side of the road around 4 a.m. the night Lisa disappeared told ABC News police questioned him again on Monday.
"Yesterday they showed me a paper with six pictures on it," Thompson said. "And I picked out the man they had been showing pictures of."
The man in the photograph has been questioned by the police several times, but the other witnesses, a couple who live three houses down from the Irwin house, said the photo did not match the man they say they saw with a baby the night Lisa disappeared.
"No, I don't recognize him," the woman said when shown the photo. "He was tall and slender and, as far as his head, we thought he was bald."
Baby Lisa has been missing since the night of Oct. 3 and an anonymous benefactor is offering a $100,000 reward for her safe return or the conviction of whoever took the little girl.