A Texas man charged with the murder of his pregnant ex-girlfriend and her 7-year-old son allegedly said he suffocated them before transporting the bodies in the woman's SUV, according to court papers.

Stephen Dale Barbee (search), 37, who led police to the scene of a "shallow grave" where authorities found two bodies believed to be that of bagel shop owner Lisa Underwood (search ) and her son, admitted to arguing with her over leaving his wife, according to court documents.

"We know that the grave contains the bodies of a female and a male consistent with the ages of Lisa Underwood and her son Jayden," Lt. Gene Jones, spokesman for the Fort Worth Police Department (search), said at a Tuesday press conference held in a Denton County field near where the bodies were found.

Barbee allegedly said he suffocated Underwood, then did the same to the boy after he interrupted the attack, court papers said. The documents said Barbee was the father of Underwood's fetus.

Barbee was arrested Tuesday in Tyler, 120 miles east of Fort Worth, where he had been working clearing trees. He was charged with murder and his bail was set at $2 million.

Barbee told investigators he put the bodies in the back of Underwood's sport utility vehicle and dug a shallow grave. The SUV was found in a creek near the town of Denton on Monday.

Court papers also revealed that a sheriff's deputy briefly had Barbee in custody early Saturday when he stopped a suspicious man covered in mud. The man ran into the woods and escaped.

Police had searched Barbee's Fort Worth home for clues into the disappearance of Underwood and Jayden. "We do know that Ms. Underwood and Mr. Barbee were romantically involved at one time," Jones said. "We don't know what the current status of their relationship is."

Jones said Jayden's father had also been contacted by police and was cooperating with the investigation.

Underwood, a popular bagel shop owner, and her little boy vanished this weekend from their Fort Worth home, where a pool of blood, but no sign of forced entry, was found. Late Monday, investigators removed a roll of carpet from the red brick home, which remains surrounded by police tape.

An Amber Alert was issued this weekend when Underwood and her son failed to show up for her own baby shower Saturday. On Monday, authorities found her missing SUV submerged in a creek.

Authorities focused part of their investigation to look for clues near the creek where Underwood's car was found. The blue Dodge Durango was discovered by a landowner just outside Denton, about 34 miles north of Fort Worth along Interstate 35, the major thoroughfare leading north to the Oklahoma state line. Police declined to say what, if any, evidence was found inside. The keys to the vehicle were found nearby.

Officers on horseback rode up and down surrounding farmland for hours after the SUV's recovery Monday morning, but ended the day without finding Underwood or Jayden, a first-grader described as the light of his mother's life.

"They are each other's lives," Marla Hess, Underwood's aunt, told the Fort Worth Star-Telegram for Tuesday editions. "They created a world that no one else can penetrate. We are going to find them together — regardless."

Underwood was a co-owner of Boopa's Bagel Deli (search) with Holly Pils, who said she last spoke with Underwood on Friday night.

Pils said "Boopa" was the nickname Underwood's mother had given Jayden.

"He wanted to be referred to as one of the owners because he said, 'My name is on the building,'" Pils said.

Well wishes piled up at the bagel shop. Several notes were taped to the inside window and a large brown teddy bear was placed on a table by the window. One of the notes said, "God Bless Lisa and her two little angels."

Outside the family home, someone wrote a chalk message on the concrete, wishing them a quick return.

FOX News' Catherine Donaldson-Evans, Phil Keating, Heather Scroope and The Associated Press contributed to this report.