(CNN) A stepfather's account of how a 4-year-old Houston girl was abducted "changed multiple times," and detectives with one of the investigating police departments believed the story "did not add up," a police spokesman says.

Texas police have been looking for Maleah Davis since the weekend , after her stepfather Darion Vence reported that strangers knocked him out and eventually took off with Maleah.

But Vence's story changed multiple times during his interview with Sugar Land police, one of the agencies involved in the case, Sugar Land police spokesman Doug Adolph told CNN on Wednesday.

"His story did not add up," Adolph said, without elaborating on why it didn't add up, or in what ways the story changed.

Asked for clarification, Adolph later said he couldn't go into specifics, but "the substantive details of what he described to us changed."

"I can say that fundamental parts of his story changed throughout the course of our initial interview," Adolph said.

CNN is attempting to reach Vence for comment. No one has been arrested or charged in the girl's disappearance.

Houston police are leading the investigation. Sugar Land is a city just southwest of Houston.

Here's everything we know about how Maleah was reported missing:

The stepfather says men abducted him and two kids, and he kept passing out

An Amber Alert was issued for Maleah Davis on Sunday morning.

Houston police issued an Amber Alert for Maleah on Sunday, after Vence reportedly told investigators of a complicated abduction that began Friday.

Vence told detectives that he, Maleah and his son were on their way to an airport Friday night to pick up Maleah's mother, who was flying in from Massachusetts, Houston police Sgt. Mark Holbrook said.

While on the road, Vence heard a "popping noise," like a popped tire, and pulled over to check on it, he told police. That's when a blue pickup truck pulled up behind the car and two Hispanic males got out, according to Vence's narrative to police.

One of the men commented, "Maleah looks very nice, looks very sweet," according to Vence's account.

The other man hit Vence in the head and he lost consciousness, he told police.

Stepfather Darion Vence says one of the abductors hit him in the head.

At some point when he woke up, Vence said he was in the back of the truck with Maleah and her brother, and three Hispanic males were also in the vehicle.

He told police he was in and out of consciousness until about 6 p.m. Saturday, when he woke up on Highway 6 with the 1-year-old boy. Maleah was not there.

Vence said he walked to a nearby hospital, in Sugar Land, where he received treatment and reported her missing.

The stepfather's story has "a lot of blanks," Holbrook said, but he said he's hoping the public can help them "fill in the blanks" in the narrative provided to them by Vence.

These are the vehicles police are looking for

Police posted a representative photo of the blue pickup truck that Vence said the abductors were driving.

Police say a blue truck similar to this one may have been used in the abduction of Maleah Davis.

An Amber Alert describes the car as a blue, crew-cab Chevy pickup truck, possibly a 2010 year model.

The car Vence was driving -- a silver Nissan Altima belonging to Maleah's mother -- is also missing, police said.

A traffic camera captured an image of the Altima driving through an intersection in Sugar Land just before 3 p.m. on Saturday, Houston police said.

This image captures the Nissan Altima on Saturday, during the time Vence said he was in and out of consciousness.

Maleah is about 3 feet tall and weighs 30 to 40 pounds. She was last seen wearing a light blue Under Armour jacket, blue jeans and gray Under Armour tennis shoes with pink and white details.

Houston police ask anyone with information about the case to call 713-308-3600.