Seth Johnson fell ill while his parents were out of town, but they decided to pray for him instead of ringing for help.

An American couple accused of killing their 7-year-old son have fled to New Zealand.

Timothy and Sarah Johnson are accused of gross misdemeanour child neglect for failing to get medical help for their adopted son, Seth, who died in March 2015.

The Johnsons didn't show up at their first court appearance Tuesday in Hennepin County, Minnesota. Assistant Hennepin County Attorney John Halla told Judge Gina Brandt that the couple has moved to New Zealand. Brandt issued warrants for their arrests.

Criminal complaints said Seth had an inflamed pancreas, possible infections and bruises on his body when he died. The Star Tribune reported the Johnsons told investigators they relied on their own research to deal with Seth's illness and didn't want him on any medication.

According to the criminal complaint, Seth, who first joined the Johnson family through foster care and later was adopted, was severely underdeveloped physically and had numerous scrapes and bruises on his body at the time of his death, the Tribune reported.

His parents said he had stopped sleeping in the weeks before his death and was always hurting himself.

The couple decided Seth was suffering from post-traumatic stress disorder, a brain injury and was a victim of fetal alcohol syndrome, but they did not seek medical help as they had "issues with going to doctors", the charging documents said.

On the weekend before the boy's death, he was being watched by his 16-year-old brother while the Johnsons were out of town. The teen called them, saying Seth wasn't eating, talking and couldn't get out of bed.

When they got home, Seth was unresponsive. "They prayed for his health", the complaint read.

They said they contemplated seeking medical care but decided to wait until morning.

The next morning, Tim Johnson found Seth unresponsive on the mattress and covered in vomit. They then called emergency services.

The Johnsons shared their grief online, writing about how faith got them through their overwhelming grief. They also started a fundraising page that featured a photo of Seth, their "very quiet and hurting little boy."

They wrote that their "bright and beautiful boy died unexpectedly."

 - AP