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People continue to leave flowers, candles and letters outside the Yates family home

HOUSTON, Texas (CNN) -- The defense lawyer for the Texas woman accused of drowning her five children said he is considering an insanity plea for his client, Andrea Yates.

Attorney George Parnham emphasized the role of mental health considerations in the case. During an interview Saturday, he said he was talking to Yates' relatives and friends and reviewing her medical records.

Asked by a reporter if he is considering a plea of insanity, he said: "It's been less than 24 hours since I've been on this case and it is too early for me to be able to give you a definitive yes, no or even maybe ... but it appears that this is where we're headed."

Police have said Yates confessed to killing her children, ranging in age from six months to seven years of age.

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Parnham predicted the prosecution would seek the death penalty. "I certainly hope not, but I'm realistic about it," he said.

Funeral services for the children are set for Wednesday at 10:30 a.m. (11:30 a.m. EDT) at Clear Lake Church of Christ.

VIDEO CNN's Ed Lavandera has more on the tragic events that occurred in Houston, Texas (June 25) Play video (QuickTime, Real or Windows Media)   VIDEO Russell Yates pledges to stand by his wife. CNN's Ed Lavandera reports (June 21) Play video (QuickTime, Real or Windows Media)   ALSO Mom accused of killing kids kept under close watch   Newspapers tell how mother allegedly killed kids   Houston prosecutor: 'I've never seen anything like this'     ON THE SCENE Ed Lavandera: Community copes with children's deaths

In a makeshift memorial to the slain youngsters, flowers, candles, stuffed animals and messages are piling up in the front yard of the Yates family home.

Yates remained Sunday under close psychiatric supervision in a special wing of the Harris County jail. She met with Parnham and several members of her family -- including her husband and mother -- Friday at the jail.

"The family is extremely supportive," Parnham told reporters after the meeting. "They are unified in seeing her through this process."

Yates, 36, appeared briefly before a judge in a Houston court Friday, a day after she was charged with capital murder. Police went to her home Wednesday and found her five children dead. Yates confessed to killing them, police said.

Under Texas law, she could face the death penalty if convicted of capital murder.

Prosecutor Joe Owmby said the capital murder charge entered Thursday is for killing in the same action two people, her sons Noah and John. Owmby said more charges for the other three deaths could come later.

Harris County prosecutor Kaylynn Williford said Yates is scheduled to appear next in court July 24. Yates was being held without bond. Authorities said she was cooperating with investigators and answering their questions.

Quoting a police official, The Dallas Morning News reported that Yates told police she had begun thinking about killing her children several months ago because she believed she was a bad mother and that her children were "not developing normally."

At a vigil held by friends and neighbors Friday night outside the Yates home, Russell Yates, the children's father, told one woman his wife was "hurting."

Yates attorney George Parnham

"She's really hurting. She's really hurting, it's really bad. It's terrible," he said, crying. Russell Yates has said his wife suffers from postpartum depression and said his wife's latest bout with depression emerged during the past three weeks, when she became withdrawn and "robotic" in her movements.

She gave birth to the couple's fifth child, a daughter, six months ago. Russell Yates said his wife's father died about three months ago, a loss that affected her.

Police said that when they were called to the Yates' home, located in the Houston neighborhood of Clear Lake, about 20 miles southeast of the city's center, the woman confessed to killing Noah, Paul, John, Luke and Mary Yates.

She then led the police to a bedroom where the lifeless bodies of 6-month-old Mary and three of her brothers -- ages 2 to 5 -- were laying on the bed with a sheet over them, authorities said. A fifth body, that of 7-year-old Noah, was found by an officer in the bathtub. Russell Yates, a NASA computer specialist at nearby Johnson Space Center, said his wife called him at work Wednesday and told him to return home.

Concerned by the tone of her voice, he asked if anyone was hurt. She responded yes, telling him it was the children, "all of them."

When he arrived at home he found police on the scene and his children dead.