Updated

A Dallas man accused of drowning his two young sons Monday after abducting them while they were walking to school with their mother was being held on capital murder charges, authorities said.

Naim Muhammad, 32, was held on $2 million bond Monday evening in Dallas County Jail on two counts of capital murder. Online jail records didn't indicate if he has an attorney.

Police identified the boys as 5-year-old Naim and 3-year-old Elijah. They have their father's last name, but police have spelled it differently than court and jail records.

A police report said the 32-year-old Muhammad forced his 3- and 5-year-old sons and their mother into his vehicle Monday morning by threatening her with a brick.

She jumped out of the vehicle after it stopped at an intersection when she saw a Dallas constable drive up. She told police that when she got out of the vehicle, the suspect jumped the curb and took off. The constable did not chase the suspect but called police, according to the report.

Police said that while they weren't able to reach the suspect on his cell phone, he did call relatives.

Hours after the boys were taken, authorities received a 911 call from a woman who said her son had drowned her grandchildren and that she had the children, who were unresponsive, in her car awaiting paramedics, Dallas Fire-Rescue spokesman Jason Evans said in a statement.

Muhammad's mother, Naimah Muhammad, told KDFW television station in Dallas-Fort Worth that when she located her son she asked to see the children and he took her to a creek.

"At first when I saw them I was saying, 'It can't be true! It can't be true!' But once he got them out of the creek and brought them to my car, and I seen they was dead I knew it was true," she told the television station. "That's when I called 911 and told them I had my grandkids and they're dead."

The boys were pronounced dead at a hospital.

The children's mother told police that the suspect told her he was going to kill the children. She also told them that he had previously threatened her life and the lives of the children.

Muhammad also tried but failed Monday to take his youngest child, a 1-year-old, from another location, Police Deputy Chief Craig Miller said at a news conference.

Miller said there was a "continuing family violence situation" between Muhammad and the boys' mother.

Muhammad was previously convicted of violent behavior.

In September 2009, he pleaded guilty to aggravated assault with a deadly weapon, a second degree felony, and received five years' probation. According to court records, the charge stemmed from a complaint from his sister that he had struck her in the head with a hammer.

Muhammad also has convictions for burglary of a vehicle, theft by check and marijuana possession, according to the Texas Department of Public Safety's online data base.

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Associated Press writer Danny Robbins contributed to this report.