When asked to comment, Biryukova's attorney would only tell ABC News, "My office does not comment about ongoing investigations."
Metalwala, who has agreed to take two polygraph tests, again today denied he has any involvement in his son's disappearance.
"I don't know what happened," Metalwala said. "If I knew I wouldn't be here."
Biryukova has refused to be tested, telling investigators that she has been too disturbed to participate.
There has not yet been enough evidence to name Biryukova as a suspect, Johnson said, but more discrepancies are appearing in her story.
The car she says ran out of gas ran fine on Friday when police took it for a test drive. No gas was added before the test and no mechanical problem was found during the drive, according to police.
Police also say Biryukova never bought gas at the Northtowne Chevron Service she and her daughter walked to on Sunday but, instead, spent time walking around a wealthy neighborhood where she reportedly didn't ask anyone for help.
Both Metalwala and Biryukova were cited for reckless endangerment in a December 2009 incident in which a then 3-month-old Sky was left in the family's SUV in a Target parking lot for 55 minutes on a 27-degree day, court records showed.
The case was dismissed earlier this year after the pair completed a year of probation, 40 hours of community service and a 10-week parenting class.
Police have received more than 900 tips so far about the missing toddler, but none of them have resulting in any solid leads. Even so, investigators are encouraging the public to continue coming forward.
"I want to stress the importance of every possible piece of information that's out there. We would really like people to err on the side of reporting information," Johnson said.
Anyone who sees a child matching this description is asked to call 911 immediately. Police are urging anyone who might have traveled along 112th Ave N.E., between I-520 and NE 24th Ave N.E., Sunday morning between 7:00 a.m. and 10:00 a.m. to call Bellevue, Wash., police at 425-452-2564 or email firstname.lastname@example.org.