Zakieya Latrice Avery, 28, of Germantown, is charged with first-degree murder in the stabbing deaths of the children, ages 1 and 2.
Montgomery County police responded to Avery's home Friday morning following a neighbor's 911 call. Police said they found the two children dead and two other siblings, ages 5 and 8, injured with stabbing wounds.
"She thought the devil was in the kids, and that's sort of the thing she centered it around as to why she had to conduct an exorcism," said Capt. Marcus Jones, director of the police department's major crimes division. "She just thought that there were evil spirits within the kids."
Another woman charged in the killings, Monifa Denise Sanford, 21, made similar statements during questioning, police said.
Sanford was arrested Saturday. The two women had been living together at the house in recent months.
Jones said the father of the children does not live in the area and is separated from Avery, but was returning to be with the surviving children, who remained hospitalized Sunday.
Both women were being held without bond on charges of first-degree murder and attempted first-degree murder and are not expected to appear in court until Tuesday afternoon. Court records do not list lawyers for the women.
Police said officers went to Avery's row house community north of Washington, D.C., early Friday when a neighbor called 911 after noticing a car with the door open and a knife lying outside of the vehicle.
Officers recovered two knives from the home. The children died from multiple stab wounds, Jones said.
Jones said the women are believed to have met each other at a church, which he identified as Exousia Ministries in Germantown.
The pastor of that congregation, Darryl Jones, declined to discuss the case after services at an elementary school Sunday or even confirm that the women worshipped there.
"This is a tragic situation. We're keeping the family in (our) prayers and we are respecting the privacy of the family," he said.
Avery's stepgrandmother, Sylvia Wade, told The Washington Post that Avery was "humble and meek" and said she loved her children.
"I don't know what triggered it. She wasn't herself. When a person is not of themselves, they are not responsible for what they are doing. They are in another zone."