Two men questioned early in the search for NBC’s Today Show host Savannah Guthrie’s missing mother said they will file a $3.25m wrongful arrest lawsuit against the sheriff who detained them, as the investigation passes the six-month mark this weekend.

Nancy Guthrie, 84, was last seen safe while at her Tucson, Arizona, home on 1 February. Authorities, including the FBI, believe she was kidnapped. But despite a number of leads and blood spatters at the house, no further trace of her has been found, and no suspects have emerged.

The Pima county sheriff’s department posted a message on social media on Thursday to mark the six-month milestone, saying: “The Guthrie investigation remains active and ongoing”, and renewing an appeal for credible information.

Savannah Guthrie, a household name in the US, meanwhile posted a video to her Instagram account earlier this week saying her family had “done our part”, but was still in agony at the matriarch’s disappearance. The case, the 54-year-old TV anchor said, was “a nightmare that will not end”.

On Thursday, it was reported by NBC News that two men who were detained and questioned in the days immediately after Nancy Guthrie vanished had issued a “notice of claim” against the Pima county sheriff, Chris Nanos, and a detective on the case.

The action, a precursor to a full lawsuit, was dated Monday and obtained by the NBC affiliate KVOA of Tucson. According to the outlet, it alleges wrongful arrest, and reputational and property damage.

The plaintiffs are Carlos Palazuelos, who was detained on 10 February for questioning and released later without charge, and Daniel Maddox, who was placed in handcuffs outside the home that belonged to his mother, Josefina, which was then searched and allegedly damaged by investigators.

Maddox was also released without charge after several hours of questioning, and is seeking $500,000. His mother is claiming $250,000 for property damage.

Palazuelos, the action asserts, is innocent, but his home was “ransacked” and his detention and subsequent questioning caused “physical, emotional and reputational harm”. He is seeking $2.5m.

Nanos, the action said, posted on social media that a person had been arrested, and that “the subject is currently being questioned in connection to the Nancy Guthrie investigation”.

That post, in conjunction with statements from the sheriff’s office, made Palazuelos look like a suspect to the world, the notice said, according to NBC.

Nanos came under scrutiny early in the investigation for the way he was handling Guthrie’s disappearance. He became entangled in a spat with the FBI over claims he had withheld crucial evidence from federal investigators, an allegation he strongly denied.

He survived a move to oust him from the case in May, and this week reignited the feud with the FBI director, Kash Patel, who claimed in June that agents “showed up immediately and offered our assistance. We were not let in for four days.”

Nanos denied that claim in an appearance on the Sharpe Exchange podcast this week, telling host Wyatt Sharpe that Patel was “misinformed”, and that the two had never spoken face-to-face. “When information is put out there that’s not accurate, it hurts the case,” he said.

The Guthrie family has offered a $1m reward for information leading to their mother being found. The FBI has put up an additional $100,000 reward for conclusive information, and has said it is looking for a man approximately 5ft 9in to 5ft 10in tall with an average build.