Asked by a reporter if Guterres was "reluctant" to take on the India-Pakistan situation which is becoming a "flash-point for a nuclear war", Dujarric said: "There is no reluctance on the part of the Secretary-General."
"Contacts are being had at various levels and we urge all parties to exercise maximum restraint," he said.
"We are very well aware and following the situation with a lot of concern," he added.
Dujarric said that Pakistan's letter to the Secretary-General about the situation in Kashmir had been received and will be circulated to members of the Security Council as requested.
According to media reports, Pakistan's Foreign Minister Shah Mehmood Qureshi had written to Guterres about the "material changes" in Kashmir and cited Security Council resolutions on the matter.
Pakistan's Permanent Representative Maleeha Lodhi tweeted that she had met Joanna Wronecka, the President of the Security Council, told her about "the grave threat to regional peace and security".
Meanwhile in Geneva, UN High Commissioner for Human Rights Michelled Bachelet's Spokesperson Rupert Colville said: "We are deeply concerned that the latest restrictions in Indian-Administered Kashmir will exacerbate the human rights situation in the region. The fact that hardly any information at all is currently coming out is of great concern in itself."
"What we are now witnessing in Indian-Administered Kashmir takes what was already a bit of a pattern to a new level," he said.
He asserted that the restrictions on communications and detention of leaders in Kashmir were a violation of the International Covenant on Civil and Political Rights that India had signed.
General Assembly President Maria Fernanda Espinosa's Spokesperson Monica Grayley said that the official who is travelling was following the Kashmir situation and was looking forward to being briefed about it by the Secretary-General when she returns to New York.
She declined to directly answer a question if Espinosa had a comment on what a reporter said were violations of Security Council resolutions.
(Arul Louis can be reached at arul.l@.in and followed on Twitter @arulouis)
( With inputs from IANS )