The Secretary-General's remarks came after India on Monday revoked Article 370 to withdraw the special status to Jammu and Kashmir and bifurcated the state into two Union Territories - Jammu and Kashmir and Ladakh.
Pakistan termed the Indian action as "unilateral and illegal", and said it would take the matter to the UN Security Council.
"The Secretary-General has been following the situation in Jammu and Kashmir with concern and makes an appeal for maximum restraint," Guterres' spokesman Stephane Dujarric said.
Stephane Dujarric specifically said that the Secretary-General "also recalls the 1972 Agreement on bilateral relations between India and Pakistan, also known as the Simla Agreement, which states that the final status of Jammu and Kashmir is to be settled by peaceful means" in accordance with the Charter of the United Nations.
The Secretary General did not offer his good offices nor did he make any offer to mediate between India and Pakistan on Kashmir.
Instead, he referred to the Simla Agreement, which is a bilateral agreement between India and Pakistan and rejects any third-party mediation in the issue.
Antonio Guterres also called "on all parties to refrain from taking steps" that could affect the status of Jammu and Kashmir.
He said the position of the United Nations on the region was governed by the Charter of the United Nations and is applicable to Security Council resolutions.
When asked to be more specific about reference to the UNSC resolutions on Kashmir in the statement, Stephane Dujarric said "I'm not going to go into any more specifics of the statement which also refers to our concern" about reports of restrictions in Kashmir in India.
"So I'll refer you to the statement," he said.
Stephane Dujarric reiterated that Antonio Guterres and the UN Secretariat were following the situation "very closely".
He said there had been contacts from the UN Secretariat both with the Indian and Pakistani authorities and with the Permanent Missions of India and Pakistan.
He said there is no plan for the Secretary-General to brief the Security Council on Kashmir.
Reacting to India's move, Pakistan expelled the Indian envoy and downgraded its diplomatic ties with New Delhi.
India has said that Jammu and Kashmir is an integral part of India and the issue was strictly internal to the country.