In reply to questions at his daily briefing, Dujarric said: "We are following with concern the tense in the region. We are also aware of reports of restrictions on the Indian side of Kashmir. We urge all parties to exercise restraint."
"We are very concerned about the rise of tensions," he said.
A communications blackout and a curfew-like restrictions have been imposed in Kashmir and several local leaders are reportedly under arrest.
Asked by a reporter if Guterres intends to play a role in resolving the issue, Dujarric said: "He has often expressed his position on that and his position remains the same."
Guterres has said that he was willing to mediate if asked by both sides. India has rejected any outside involvement in the dispute, which it says has been accepted by Pakistan as a bilateral issue.
Dujarric also said that over the past few days the UN Military Observer Group in India and Pakistan (UNMOGIP) "has observed and reported an increase in military activity along the Line of Control".
Asked if the UN had any information if the International Court of Justice had received a complaint from Pakistan about the revocation of Article 370 of the Indian Constitution, he said: "We would not have that information."
General Assembly President Maria Fernanda Espinosa reiterates "that tension in this region doesn't benefit anyone, her Spokesperson Monica Grayley said.
(Arul Louis can be reached at arul.l@.in and followed on Twitter @arulouis)
( With inputs from IANS )