A 37-year-old man was ordered held without bail Monday after he allegedly poured lighter fluid over his girlfriend and their 1-year-old baby on Saturday and threatened to light them on fire, according to Lawrence police.

William Connatser of Lawrence was charged with two counts of assault and battery on a household member; two counts of assault to murder; attempting to commit a crime; reckless endangerment of a child; two counts of mayhem; two counts of kidnapping; and attempting to burn a motor vehicle, according to the Essex district attorney’s office.

Connatser was in the Essex County sheriff’s prerelease program and wearing an ankle bracelet at the time of the alleged assault, according to police. He had asked for permission to go to Market Basket on Saturday morning, and it was there that he purchased the lighter fluid and met with his girlfriend, police said.

Lawrence Police Chief Roy P. Vasque said Connatser and his girlfriend were inside a vehicle when they got into an argument and he began to douse her and the toddler with lighter fluid. He started flicking a lighter and told her to drive, he said.

As they were driving she saw a police cruiser and began honking the horn in an effort to get the officer’s attention, Vasque said. Connatser then started “punching her about the head and face,’’ he said.

A witness to the assault flagged down Officer Jesse Fabian on Broadway near Essex Street at approximately 10:09 a.m. Saturday, and Fabian immediately intervened.

Vasque said Connatser was hitting his girlfriend and Fabian ordered him out of the vehicle at gunpoint. Connatser was placed under arrest, and the woman and child were taken to the hospital, he said.

The woman was bleeding and suffered “severe injuries’’ to her face, according to police.

Vasque commended the victim for beeping the horn and seeking assistance from the police.

“It took a lot of courage and strength’’ to seek the assistance of the police, he said.

Vasque also praised the actions of the officer who got Connatser out of the vehicle.

“This was a very volatile situation . . . [the officer] made the right decision,’’ he said.

Their actions very likely averted what could have been a tragic situation, he said.

Connatser was ordered held without bail Monday at his arraignment in Lawrence District Court pending a dangerousness hearing scheduled for March 21, according to Carrie Kimball Monahan, a spokeswoman for the Essex district attorney’s office. He was ordered to have no contact with the alleged victims and abide by a restraining order, she said.

Emily Sweeney can be reached at esweeney@globe.com. Follow her on Twitter @emilysweeney.