Francisco Oropesa, who is considered to be armed and dangerous, is believed to have fled the rural town of Cleveland on foot after the shooting on Friday night.

Neighbours have said the Mexican national had lived on the street where the shooting took place for years.

The attacks took place after the 38-year-old's neighbours asked him to stop firing off rounds in his garden late at night because a baby was trying to sleep.

The gunman's victims were all from Honduras and have been identified as Diana Velazquez Alvarado, 21; Julisa Molina Rivera, 31; Jose Jonathan Casarez, 18; Sonia Argentina Guzman, 25; and Daniel Enrique Laso, 9.

More than 250 law enforcement officers from multiple agencies, including the US Marshals, are now part of a growing search.

Oropesa has not been found despite scent-tracking dogs, drones and a total of $80,000 (£64,000) in reward money on offer.

An FBI agent on the scene near Houston has acknowledged the bureau has little to go on in the widening manhunt.

On Monday, a heavy police presence converged in Montgomery County after a possible sighting, but the sheriff's office later said none of the people located were Oropesa.

A few hours later, the department reported another possible sighting, tweeting that several schools had "secured their campuses" and again asked residents to avoid the area.

But that search, too, turned up nothing.

Both were among the first times since the shooting on Friday night that authorities had announced a possible sighting.

Wilson Garcia, the father of the one-month-old who had been crying before the shooting, has described the terrifying moments his wife Sonia Argentina Guzman and nine-year-old son Daniel Enrique Laso were gunned down.

He said he and the three other men went to Oropesa's home and "respectfully" asked him to curtail or move his target practice.

"He answered by saying he was in his property and could do whatever he wants," Mr Garcia said.

"Then he began insulting us... My wife said, 'OK, let's call the cops.' Police took, like, 20 minutes to arrive, and we called five times because the man was very threatening," he added.

It wasn't clear whether all five of the 911 calls came before, during or after the shooting.

After refusing to stop firing, Mr Garcia said he could see Oropesa on his porch "smoking and drinking something" before "we saw him as he went inside his home to load the gun".

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Mr Garcia said he urged his wife to take cover inside as the gunman approached their house but she stood her ground.

He said: "He just walked in shooting. He didn't say anything. He shot her, and the door was wide open. He walks in, room by room, shooting at us."

Daniel ran to his fatally-wounded mother but was also gunned down, Mr Garcia said.

Police have recovered an AR-15-style rifle that they said Oropesa used in the shootings.

Authorities were not sure if he was carrying another weapon after others were found in his home.

Meanwhile, Republican Governor Greg Abbott has faced a backlash over drawing attention to the victims' immigration status.

Mr Abbott offered a $50,000 (£40,000) reward over the weekend for any tips that might lead to the gunman being caught.

While doing so, he described all the victims as "illegal immigrants" - a potentially false statement that his office has now apologised for.