Activists have condemned the inspections, which have targeted numerous high-profile rights groups, as a form of intimidation.
The Prosecutor General's Office said on Thursday that the inspections are part of efforts at ensuring compliance with anti-extremism laws and combating the legalization of illegal income.
But Putin said the checks should be monitored by the presidential ombudsman for human rights, Vladimir Lukin, to ensure there were no "excesses.”
Lukin should keep the situation "under control” and act "as a source of additional information” for the president’s office, Putin said.
The Prosecutor General's Office says it will examine any reports of violations during inspections.
According to legal rights group Agora, which has provided support to many political activists and the Pussy Riot punk band, more than 80 organizations across 24 regions have been audited.
Agora director Pavel Chikov, who is a member of the Presidential Council of Human Rights, said on Thursday that inspections primarily targeted groups dealing with human rights and environmental issues, as well as organizations that influence public opinion.
The fiercely pro-Kremlin broadcaster NTV has been in attendance at several unannounced raids, prompting fears that some groups may later be subjected to a smear campaign. NTV has in recent years produced several lurid and sensationalist documentaries criticizing government critics.
Earlier this week, state agencies confiscated a stack of documents from the offices of Amnesty International and paid a second visit to the Memorial rights group.
Also among those targeted this week were two German organizations: the Friedrich Ebert Foundation (FES) and the Konrad Adenauer Foundation (KAS), a political think tank with ties to German Chancellor Angela Merkel's Christian Democratic Union party.
Human Rights Watch and several regional offices of the French Alliance Française, an international organization promoting French language and culture, were also subjected to checks.