The Pakistan military's spokesman denied any violation of the ceasefire, agreed last week.
India's Director General of Military Operations was speaking as a fragile 24-hour-old ceasefire appeared to be holding after both sides blamed the other for initial violations on Saturday night.
"No violation is being made by the Pakistan army or armed forces of the ceasefire," Pakistan's military spokesman said during a press conference.
The truce announced on Saturday followed four days of intense fighting between the nuclear-armed neighbours. In the worst fighting in nearly three decades, they fired missiles and drones at each other's military installations, killing almost 70 people.
Diplomacy and pressure from the United States helped secure the ceasefire deal when it seemed that the conflict was spiralling alarmingly.
But within hours of its coming into force, artillery fire was witnessed in Indian Kashmir, the centre of much of last week's fighting.
Blasts from air-defence systems boomed in cities near the border under a blackout, similar to those heard during the previous two evenings, according to local authorities, residents and Reuters witnesses.
"Sometimes, these understandings take time to fructify, manifest on the ground," Indian army chief Lieutenant General Rajiv Ghai told a media briefing, referring to the truce.
"The (Indian) armed forces were on a very, very high alert and continue to be in that state."
The Indian army chief had given a mandate to its commanders to deal with "violations of any kind" from across the borders in the best way they deem fit, Ghai added.
He said his Pakistani counterpart called him on Saturday afternoon and proposed the two countries "cease hostilities" and urgently requested a ceasefire.
Following India's request for a call after carrying out military attacks in Pakistan between May 6 and 7, and on the intervention of international interlocutors, Pakistan responded on May 10 to the earlier request, said Pakistan's military spokesman.
Late on Saturday, the Pakistani foreign ministry had said it was committed to the truce agreement and blamed India for the violations.
US President Donald Trump announced the ceasefire on Saturday, saying it was reached after talks mediated by Washington.
US Secretary of State Marco Rubio said India and Pakistan had also agreed to start talks on "a broad set of issues at a neutral site".
On Sunday, Trump praised the leaders of both countries for agreeing to halt the aggression and said he would "substantially" increase trade with them.
Hindu-majority India and Muslim-majority Pakistan each rule a part of Kashmir but claim it in full, and have twice gone to war over the Himalayan region.
India blames Pakistan for an insurgency in its part of the territory, but Pakistan says it provides only moral, political and diplomatic support to Kashmiri separatists.
Among those most affected by the fighting were residents on either side of the border, many of whom fled their homes when the fighting began on Wednesday, two weeks after a deadly attack in Indian Kashmir's Pahalgam that India said was backed by Islamabad.
Pakistan denied the accusation.