A man accused of sending texts to the Guthrie family with "intent to transmit a demand for ransom" has been arrested in Los Angeles.

According to a criminal complaint filed in the US District Court of Arizona, Derrick Callella allegedly admitted to authorities that he sent the messages using a voice over internet protocol (VoiP) application after seeing TV coverage of Nancy Guthrie's disappearance.

The complaint said that he told officials he was just "trying to see if the family would respond".

Callella is facing a charge of intent to transmit a demand for ransom and a charge of utilising a telecommunications device to anonymously abuse, threaten or harass.

The two messages are not linked to Monday's reported ransom demand. Investigators are taking that ransom note seriously, said Heith Janke, the FBI chief in Phoenix, who noted it included a demand for money with a deadline, along with details about a floodlight at the home and an Apple watch.

At least three media organisations have reported receiving purported ransom notes that they handed over to investigators.

"To anyone who may be involved, do the right thing. This is an 84-year-old grandma," Janke said.

Authorities say any decision on ransom demands is ultimately up to the family.

Pima County Sheriff Chris Nanos has revealed that DNA tests showed blood found on Nancy Guthrie's porch had come back as a match to her.

"Right now, we believe Nancy is still out there. We want her home," Nanos said at a news conference.

The sheriff acknowledged that authorities have no proof she is still alive.

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