"Nothing at this point indicates we have had criminal activity, but we are not ruling that out," Swanton said.
A U.S. intelligence official told CNN there is no indication so far that the blast is related to terrorism.
While state authorities are leading the investigation, the federal government is assisting.
The Federal Bureau of Alcohol, Tobacco, Firearms, and Explosives has a team of 20 agents and forensic specialists assisting, a law enforcement source told CNN.
The Texas National Guard has sent 21 troops from a civil support team to monitor air quality near the blast, the Pentagon said Thursday.
The White House said it is monitoring the situation through the Federal Emergency Management Agency, which is in touch with various agencies involved in the investigation.
"A tight-knit community has been shaken, and good, hard-working people have lost their lives," President Obama said in a statement.
Those affected "will have the support of the American people," he said.
With help from heavy rains early Thursday, firefighters managed to quell most of the flames in the area, authorities said.
The rain and heavy winds also helped dissipate chemicals that may have been released.
Swanton emphasized that there was no cause for alarm about the air. There was no "chemical escape" that is "out of control," he said.
Anhydrous ammonia, a gas used in making fertilizer, can cause severe burns if it combines with water in the body. Exposure to high concentrations can lead to death.
The West Fertilizer Co. said it had 54,000 pounds of the chemical, The Dallas Morning News reported.
But doctors reported that the injuries they were treating, in general, came from the blast, not chemical exposure. Many people had cuts and puncture wounds. Some were in critical condition.
Small, smoldering fires remained Thursday, but not enough to halt rescue efforts, police said.
There was one early report of possible looting, but no one was arrested, Swanton said.
The Federal Aviation Administration instituted a flight restriction over the town.
Local rail freight service was also being closed to help secure the area, the U.S. Department of Homeland Security said.
Authorities closed schools for the rest of the week and urged everyone to stay away from school property.
So many firefighters and medics descended on the town to help its all-volunteer force that the Texas public safety department said that no more assistance was needed.
"The firefighters and EMS people are coming from hundreds of miles away to help us," said Wilson of the department. "Right now, we are overflowing with help. "
West is about 75 miles south of Dallas and 120 miles north of Austin. The town's chamber of commerce touts it as "the Czech point of central Texas."
Czech immigrants arrived in the town in the 1880s, and the community still maintains strong ties to their Central European roots, with businesses named "Little Czech Bakery" and "The Czech Inn."