However, they refused to elaborate beyond saying the situation has been "contained".
Earlier it was revealed that the escaped prisoner was linked to the fatal shooting of two in the Pacific Island nation.
Police found Chris Rimamotu in a house on the southern part of the island and surrounded the property this morning.
The 41-year-old yesterday escaped from the Rarotonga jail yesterday and got hold of a weapon.
He is believed to have shot a man and a woman in his home district of Titikaveka, approximately 10km away on the southern part of the island.
About 30 police officers this morning scoured the area around Vaimaanga, 3km from the double shooting and where Rimamotu was last spotted in a double cab 4WD pick-up.
A witness, who had been helping police with their search, was there when Rimamotu was found about 9am local time.
"Five shots rang out and the cops retreated for cover. Police commissioner was talking to him and trying to get him out," he said.
The witness said after the shots were fired he was moved from the scene so was unable to say what is happening now.
Cook Islands police inspector John Strickland said the fugitive was armed with a .22 calibre rifle.
Strickland could not say how Rimamotu ended up armed with a weapon, but said it was not a police-issued one.
He confirmed the two who were shot yesterday evening had died, but refused to divulge any details as to their relationship to the prison escapee.
Cook Island News reported the victims were a man and a woman said to have been known to Rimamotu.
Comments on social media also indicated those that had been shot were his ex-partner and her current partner.
Strickland refuted earlier reports that Rimamotu had taken a child.
"I'd like to confirm the child is safe. There was never a child with him, it was just one of those comments from someone."
Despite Strickland's assertions a child was never involved, a police update seemed to indicate there had been concerns over a young boy's safety.
"For the concerned family out there, the boy is confirmed to be safe and arrangements have been made to keep him safe," the update on the Cook Islands Police Service page said. "Please do not ask anymore about the boy, no further information will be made available on this topic for his sake."
Strickland wouldn't indicate how Rimamotu had escaped, saying it was too soon.
"I can't put that into detail, we will have to conduct a thorough investigation. Because the matter is still fresh I don't think it's appropriate for me to say too much.
Strickland said Rimamotu had been sentenced on December 3 last year for kidnapping a "very young kid" for seven years.
He said he was unable to divulge further details.
