The three children were found dead Monday night, with police saying they bore no obvious signs of trauma.
The 22-year-old mother, Rachel Henry, "has admitted to harming her three children, which caused their demise", police Sgt. Mercedes Fortune told reporters outside the home on a block with an old mobile home, several weathered wooden houses and other buildings in a once rural area of southern Phoenix.
The mother was in the process of being booked on three counts of first-degree murder.
A relative who lives at the residence called police Monday and responding officers found a 7-month-old girl, 2-year-old girl and 3-year-old boy, authorities said.
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Responders found the three children unresponsive, and were unable to resuscitate them.
Phoenix firefighters reported the children died from drowning, but then disavowed that report, Fox 10 Phoenix reported. There is also a white Spanish-style church nearby.
Authorities say they were interviewing the mom, dad and another relative. It was not immediately clear if she had an attorney. But there is some new construction, with single-family home construction with a price of more than $ 500,000. She said the family recently moved to Arizona from Oklahoma.
Sgt Fortune says the woman, her husband and another relative all staying in the home were questioned separately to try and get an accurate account of what happened. The investigation is still ongoing.