The cousin of missing Illinois mom Lisa Stebic says her family is holding off casting blame on who may be responsible for her disappearance until evidence proves exactly what happened to her.

"The police have not told us they have a suspect," Mark Greenberg told FOX News on Monday. "The people pointing fingers at this point are the media."

Plainfield, Ill., police were able to obtain a warrant to search Stebic's home on May 14. Local news reports said they obtained the warrant because they had found traces of her blood on a tarp in her husband's vehicle.

But Dion Davi, the attorney for Stebic's husband, Craig, told FOX News that it's not yet clear whether the tarp was the cause for the warrant. Davi said that after two searches of the Stebic home earlier this month, he received from police an itemized list of what was taken from the home, which included the family computer. The tarp was not on the list for either of those two searches.

That means it may be something else police found after those two searches that prompted the May 14 warrant.

Unnamed police sources, as reported in local newspapers like The Naperville Sun and the Joliet Herald News, had said officials used the blood evidence to obtain the warrant by positing a scenario that her husband Craig, an avid hunter, might have used the tarp to transport his wife's body from the home.

Charles Pelkie, spokesman for Will County State's Attorney James Glasgow, would neither confirm nor deny the report for the Sun, saying that "the contents of the warrant are under court seal."

But FOX News confirmed that the car the blood was found in was one of the family's two vehicles, a 2002 Chevrolet S-10 pickup truck. The family's other car was a 2004 four-door Saturn Ion. Both were registered to Craig Stebic, but Lisa used the Saturn. Both have been confiscated by police.

Craig Stebic has never been named a formal suspect in the case and has been compliant with police requests, according to Michelle Sigona, a correspondent for America's Most Wanted, which has profiled the Stebics' case. Craig Stebic gave police the family's computer but would not submit to a lie-detector test on the advice of his attorney, Sigona told FOX News. His divorce lawyer has advised him against submitting to the test.

"We just have to hold out hope as long as we possibly can," Greenberg told FOX News on Monday.

He said Lisa's family was "very concerned" about the couple's children, ages 10 and 12, and how they're holding up while their mother is missing. Greenberg said Craig Stebic brought the children to stay with another relative two weekends ago to take a break from the media frenzy surrounding the case.

"It's very important we try to preserve as much of a normal life as possible for these children," Greenberg said.

On Saturday, friends and family of Lisa Stebic gathered for a candlelight vigil to mark the mother of two's 38th birthday.

Stebic was last seen at about 6 p.m. April 30 at her Red Star Drive home in Plainfield, Ill.

She disappeared while her husband — from whom she was seeking a divorce — was in the backyard and her two children were out. She was reported missing by her husband the next day. Since then, there has been no activity on her cell phone or credit cards.

The search on May 14 was the first time authorities publicly acknowledged Stebic may be a victim of foul play.

"We need to focus part of our investigation on the fact that she may not have voluntarily disappeared," Plainfield Police Chief Don Bennett told the Sun.

It was reported May 17 that Stebic was trying to have her husband evicted from their Plainfield, Ill., home so the family could "live in peace."

Stebic's petition for temporary eviction stated he was being "unnecessarily relentless, cruel, inconsiderate, domineering and verbally abusive." His behavior was "jeopardizing the mental well-being" of their children, she wrote.

Divorce proceedings began in December. The couple has lived in the same house since then but rarely spoke.

Craig Stebic's attorney, Dion Davi, denied the abuse allegations to the Chicago Tribune, noting the couple cited irreconcilable differences in their divorce action. He said Lisa Stebic was never in danger from her husband.

FOX News' Steve Brown contributed to this report.