There are at least five deceased and 21 injured in the shooting, an official of the Odessa Police Department said at a press conference.
In a Facebook post, the Midland Police Department said: "There is no active shooter at this time. All agencies are investigating reports of possible suspects."
Earlier, two people were suspected to be involved in the shootings and police had said they were believed to be driving around separately in a gold/white-coloured Toyota vehicle and a stolen US Postal Service van.
Authorities have urged the public to get off the road "and use extreme caution".
President Donald Trump said he has been briefed about the incident by Attorney General William Barr. "FBI and Law Enforcement is fully engaged," he tweeted.
Texas Governor Greg Abbott described the incident as a "senseless and cowardly attack".
"The state of Texas and the Department of Public Safety are working closely with local law enforcement to provide resources as needed and deliver justice for this heinous attack," he said in a statement.
"I thank the first responders who have acted swiftly and admirably under pressure, and I want to remind all Texans that we will not allow the Lone Star State to be overrun by hatred and violence. We will unite, as Texans always do, to respond to this tragedy," he added.
The University of Texas campus in Permian Basin told students, staff and faculty to shelter in place.
(Only the headline and picture of this report may have been reworked by the Business Standard staff; the rest of the content is auto-generated from a syndicated feed.)
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