Hillsborough, N.C. — A man accused of gunning down his estranged wife last week outside a Chapel Hill elementary school was ordered held without bond Tuesday and prohibited from contacting his children.

Ali Cherfaoui, 49, is charged with first-degree murder in the death of Chahnaz Kebaier. His next court date was set for June 11.

Kebaier, 40, was shot several times in front of Mary Scroggs Elementary School, at 501 Kildaire Road, as she was about to pick up her 5-year-old daughter and 4-year-old son from school.

Chapel Hill police said Cherfaoui shot Kebaier as the result of "an ongoing domestic dispute." Court records show that the couple married in August 2005 but separated last June.

At about the same time as they separated, Kebaier obtained a domestic violence protective order against Cherfaoui, who was barred from having contact with her and from possessing a firearm through mid-June.

The protective order states that Cherfaoui had threatened to kill his wife if she took the children and said that he was willing to be a martyr for his children.

During his first court appearance Tuesday, a District Court judge ordered Cherfaoui not to have any contact with his children or Kebaier's family. The order prohibits him from trying to send letters, emails or text messages or delivering flowers or gifts, the judge said.

Kebaier had been in the country for about 10 years. The Tunisia native had been a research associate at the University of North Carolina at Chapel Hill since 2009.

A citizen of Algeria, Cherfaoui has lived in the U.S. for about 20 years. Court papers and his arrest report show he is unemployed.

This spring, he was ordered to pay eight months of back child support, totaling almost $3,000, as well as $300 a month to remain current in his support.

The shooting sent Mary Scroggs Elementary into a lockdown, but no students or staff were harmed.

“Our hearts are breaking for the loss of Chahnaz Kebaier and for her family at this sad time," Principal Keri Litwak said in a statement released Tuesday.

“I am so proud of the way the Mary Scroggs Elementary staff worked together to ensure the safety of our students. They did an excellent job in carrying out lockdown procedures and dismissing students under extraordinarily difficult circumstances," Litwak said. "Scroggs parents and other community members also have been remarkably supportive throughout this ordeal."

Tuesday was the first day of classes at the school after the shooting and the holiday weekend, and Litwak said about 20 students and staff met with counselors.