Police in the US say 11 children aged between one and 15 were rescued in the state of New Mexico after officers raided a makeshift compound occupied by armed "extremists".

Two men were arrested after police found them and the children in what one officer called "the saddest living conditions and poverty I have seen".

The arrests were part of the operation connected to a months-long search for an abducted three-year-old, according to New Mexico's Taos County sheriff's office.

The investigation kicked off late last year on the opposite side of the country in Jonesboro, Georgia.

Siraj Wahhaj, 39, of the state's Clayton County was accused of kidnapping his toddler, who was ultimately not found.

The boy's mother told police her child, who she said suffered from seizures along with development and cognitive delays, went to the park with his father Mr Wahhaj last December and never returned.

On Thursday last week, Sheriff Jerry Hogrefe of Taos County in New Mexico issued a search warrant describing "a makeshift compound surrounded by tires and an earthen berm" in a subdivision, where Mr Wahhaj along with another man, Lucas Morten, were thought to be.

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The FBI had provided information and surveillance on the spot but "didn't feel there was enough probable cause to get on the property," Mr Hogrefe said.

"That all changed for me when a message was forwarded to us from a Georgia Detective that we reasonably believed came from someone at the compound - the message sent to a third party simply said in part 'we are starving and need food and water'," the sheriff said in a statement.

"I absolutely knew that we couldn't wait on another agency to step up and we had to go check this out as soon as possible."

The sheriff described planning "a tactical approach for our own safety because we had learned the occupants were most likely heavily armed and considered extremist of the Muslim belief".

On Friday morning, a dozen officers kicked off the "all day" operation, discovering the two men with an AR-15 rifle, five loaded 30-round magazines and four loaded pistols, including one in Mr Wahhaj's pocket.

The men at first refused to follow verbal direction, police said, who added the raid went without major incident or injuries.

Mr Morten was charged with harbouring a fugitive and Mr Wahhaj was detained on his Georgia warrant for child abduction.

Three women thought to be parents of the children now in protective custody were also detained for questioning, and were released pending further investigation.