The former Marine who shot dead famed Navy SEAL sniper Chris Kyle is still receiving $2,800 a month in Veterans Affairs benefits, it emerged in court on Tuesday.

Eddie Ray Routh, 27, is on trial for gunning down Kyle and his friend, Chad Littlefield, at a Texas shooting range two years ago. He has pleaded not guilty by reason of insanity.

Routh received $30,000 in back-pay benefits after he was arrested and will continue to get his monthly payout unless he is convicted of murder - and then he'll receive 10 per cent, around $280 a month, the New York Post reported.

On Tuesday, prosecutors quizzed his mother, Jodi Routh, on the money, which he began receiving after the VA determined he was disabled following the shootings.

Payouts: The government continues to pay accused murderer Eddie Ray Routh, pictured in court on Tuesday, $2,800 a month in Veterans Affairs disability payments, it emerged in court

Mrs Routh said it is being held in a bank account that she manages with her husband.

Prosecutors said some of the money has gone toward a down payment for a house Routh's sister bought with her husband, but Mrs Routh said she was unaware of that, the Post reported.

The matter was discussed once jurors were out of the room. District Judge Jason Cashon held a brief hearing on whether Routh was still qualified for his three court-appointed lawyers.

The judge told Mrs Routh not to touch the money, or allow anyone else to touch it. He said he will rule on the issue later this week.

On Tuesday, the prosecution wrapped up their testimony in the trial in Stephenville, Texas. On Wednesday, defense attorneys are presenting their first full day of testimony.

Mrs Routh was their first witness on Tuesday. She testified that she had reached out to Kyle for help with her troubled son after reading his book, but did not know they were going to the shooting range.

Under cross-examination, prosecutors asked Jodi Routh if she regretted not telling Kyle of threats Routh had made to kill himself and his family.

On Tuesday, Jodi Routh recounted her son's mental anguish and stints in facilities before the killings

'I was just looking for help for my son,' she responded.

Kyle, the famed former Navy SEAL sniper who served four tours in Iraq, and his friend Chad Littlefield were shot dead at the range in February 2013. Routh then stole Kyle's truck and was arrested following a police chase.

Eddie Ray Routh has pleaded not guilty, and his attorneys are mounting an insanity defense.

There is no doubt over the fact that Routh shot the men dead. Instead, the prosecution is trying to show that he was aware of what he was doing, while the defense claims he was in a psychotic state.

Family members have said he was suffering from post-traumatic stress disorder after serving in Iraq and in Haiti after the devastating 2010 earthquake.

The court has also heard how he smoked marijuana and may have consumed whiskey before heading to the shooting range with Kyle and Littlefield, but voluntary intoxication is not a defense.

Prosecutors have also contended that he knew right from wrong.

A Texas Ranger testified that authorities also found anti-psychotic medication for schizophrenia while searching Routh's home after the shooting.

Victims: Chris Kyle, left, and Chad Littlefield, right, were both shot multiple times on February 2, 2013

In court: Kyle's wife, Taya Kyle, is seen in court during the trial in Stephenville, Texas on Tuesday

Last week, a former deputy testified that he overheard Routh after he'd been taken into custody say that he shot the men because they wouldn't talk to him as the three drove together to the shooting range.

The court also heard this week how Routh became irritated when Littlefield was not shooting.

'Are you gonna shoot? Are you gonna shoot? It's a shooting sport. You shoot,' Routh said in a phone call to a New Yorker reporter after the killings. 'That's what got me all riled up.'

In his taped confession, he also said he was fearful that if he didn't shoot the men, whom he called 'headhunters', then they would turn on him.

'If I didn't take out his soul, he was going to take my soul next,' Routh said.