Dmitry Peskov also told journalists on Thursday that investigators have found no evidence to back up reports by the respected newspaper Novaya Gazeta that police in the predominantly Muslim republic rounded up more than 100 men suspected of homosexuality and that at least three of them were killed.
Mr Putin met late on Wednesday with the Chechen leader, who in the televised portion of the meeting suggested Putin should not believe the "provocative" claims.
Russian President Vladmir Putin continues to deny that gay men are facing persecution in Chechnya despite multiple media reports contradicting his claims.
CNN recently interviewed gay men who survived the camps, who detailed the abuse and torture they faced after they were detained. Cohen also asked viewers to sign a petition asking several major oil companies who do business in Russian Federation to speak out about the human rights abuses happening in Chechnya.
"Kadyrov's confirmation that everything will be done within a legal framework was of course approved by the president", he added.
When a journalist mentioned media accounts of conversations with victims, Peskov said: "Where are they?"
However the monitor said she could "pay a visit, make an inquiry and view their documents" to find out more, while insisting Russian Federation has "a mechanism to protect people who are afraid".
"These are some phantom complaints, absolutely depersonalized", Peskov said.
Prosecutors launched a formal investigation on Monday.
American flight attendant to angry passenger: 'Hit me'
An American Airlines spokesperson told ABC News that the woman passenger brought a double-wide stroller onto a single-aisle plane. But right now, American Airlines is under fire again - and there's a pretty damning video to go along with the allegations.
This is a position that appears to be shared among Chechnyan people.
But activists fear that remarks from Russian officials denying or downplaying the reports mean there is little chance justice will be done.
"Have people really suffered, or does somebody want to get something out of this?" the Interfax news agency quoted her as saying.
They called on the government to pass a resolution "The centuries-old traditions of Chechen society, the dignity of Chechen men, and our faith have all been insulted, and we promise that those behind it will face reprisals, whoever they are and wherever they are".
Cohen directly addressed Chechen leader Ramzan Kadyrov on his show about the reports, saying, "You, sir, are responsible for these crimes", Cohen said.
Kadyrov criticized the reports, which he said were "unsubstantiated", and the two then went on to discuss other things.
They maintain that they can't abuse homosexual men as gay people "do not exist" in Chechnya. Police also "outed" the men to their relatives and encouraged them to carry out "honor killings".
Government critics say the Kremlin has given him free rein because it relies on him to keep a lid on separatism and insurgent violence after two devastating post-Soviet wars in the region.