The two countries have been locked in a diplomatic clash following a suicide attack on February 14 in Kashmir that killed 40 Indian security personnel, triggering counter-operations by Indian forces in the area.
"We are deeply concerned at the increasing tensions between the two countries," said UN spokesman Stephane Dujarric.
Guterres "stresses the importance of both sides to exercise maximum restraint and take immediate steps" to de-escalate, while also offering to mediate "should both sides ask," said Dujarric.
Pakistan's Foreign Minister Shah Mahmood Qureshi appealed to Guterres to step in to defuse tensions, in a letter seen by AFP.
"It is imperative to take steps for de-escalation. The United Nations must step in to defuse tensions," said the letter sent on Monday.
The attack was claimed by Pakistan-based Islamist group Jaish-e-Mohammed (JeM), but the foreign minister insisted that "attributing it to Pakistan even before investigations is absurd."
In response to the rising tensions, France, Britain and the United States were considering a new push at the Security Council to place Masood Azhar, the leader of JeM, on the UN terror list, but faced opposition from China, diplomats said.
China has twice blocked -- in 2016 and 2017 -- attempts to put the JeM leader on the blacklist. The group itself was added to the terror list in 2001.
Kashmir has been split between India and Pakistan since independence from Britain in 1947. Both countries claim the former Himalayan kingdom in full and have fought two wars over it.
India has long accused Pakistan of harbouring militants who launch attacks on its soil.
Pakistan's UN Ambassador Maleeha Lodhi met with Guterres and with the president of the Security Council to appeal for action, warning that a flareup in Kashmir could undermine peace efforts in Afghanistan.
"The escalation in the subcontinent poses a threat to prospects for peace in Afghanistan," Lodhi told AFP.
The United States is holding talks with the Taliban on ending 17 years of war.
US envoy Zalmay Khalilzad's talks also involve Pakistan, Saudi Arabia and the United Arab Emirates, the three countries that recognized the Taliban regime in Kabul before the US-led coalition toppled it following the September 11, 2001 attacks.
Guterres 'stresses the importance of both sides to exercise maximum restraint and take immediate steps' to de-escalate, while also offering to mediate 'should both sides ask,' UN spokesman Stephane Dujarric.