Rowe's case and a handful of others are scheduled to go to trial in Criss' court Sept. 18.
BP spokesman Neil Chapman said the company will appeal her ruling.
"Neither Lord Browne or John Manzoni have unique knowledge of the Texas City incident on March 23, 2005," Chapman said. "Other BP management, more closely associated with the operations of the plant, are already assisting in the discovery process."
Workers were restarting a unit at the plant after a monthlong outage when they accidentally overflowed a splitter tower with highly flammable hydrocarbons. The materials then quickly filled up an overflow drum, then rushed up a vent stack that led to the atmosphere.
Liquids and a huge vapor cloud that had collected on the ground were then quickly ignited, likely by an idling truck, causing an explosion that was heard and felt up to five miles away.
In addition to those killed, at least 170 others were injured, although many more than that have filed suits against the company.
Federal investigators have said that the unit had a long history of safety problems; key alarms and other equipment were not working properly that day; and that workers may have been fatigued.
The U.S. Chemical Safety and Hazard Investigation Board also has said it has found evidence that BP management generally had a lax attitude toward safety.
Coon and others have already taken the depositions of dozens of BP officials, both at the refinery and in the oil giant's upper echelon.
Earlier this month he traveled to London and deposed Mike Hoffman, the company vice president of refining. But he was blocked from questioning Browne and Manzoni, he said.
Coon said he wants to talk to Browne and Manzoni because he believes "the knowledge of the problems at Texas City went to the highest of levels of BP."
Further, he said that documents and witness statements show that companywide budget cuts were ordered years before the blast, and that needed safety improvements weren't made because of them.
"I want Mr. Browne and Mr. Manzoni to take time out of their busy schedules to explain how they let all of those people get killed," Coon said.
He said the two executives should give their depositions because they "injected" themselves into the matter by personally visiting the Texas City site following the accident.
BP, which has said it has taken full responsibility for the explosion, has set aside more than $1 billion to handle claims against the company following the accident. It also has said it plans to spend that much in improvements at the plant over the next few years.
Already the company has settled with the majority of the most serious civil cases, paying families of the deceased and critically injured workers reportedly tens of millions of dollars each.
Last September, the Occupational Safety and Health Administration fined BP a record $21.4 million after finding more than 300 alleged violations of federal regulations. The company remains under criminal investigation by the U.S. Department of Justice.