Islamabad, Pakistan - Indian Prime Minister Narendra Modi has told his Pakistani counterpart that while India desires normalised relations with its western neighbour, this would require "an environment of trust, free of terror, violence and hostility".

Modi, a right-wing nationalist who was re-elected with an overwhelming majority last month, wrote a letter responding to a congratulatory message by Pakistani Prime Minister Imran Khan, the Indian foreign ministry said in a statement on Thursday.

"As per the established diplomatic practice, PM and [Foreign Minister Subrahmanyam Jaishankar] have responded to the congratulatory messages received from their counterparts in Pakistan," Raveesh Kumar, spokesman for India's foreign ministry, said.

"In their messages, they have highlighted that India seeks normal and cooperative relations with all neighbours, including Pakistan."

Tensions between the nuclear-armed South Asian neighbours have been high since February when a military standoff saw them conduct air raids on each other's territory and engage in an aerial dogfight that saw at least one Indian fighter jet shot down.

The Indian air raids, which hit near the northern Pakistani village of Jaba, were a key part of Modi's Bharatiya Janata Party's (BJP) election campaign as the prime minister vowed to continue to "punish" Pakistan.

India accuses Pakistan of supporting armed groups that target Indian security forces in the disputed territory of Kashmir and elsewhere, saying that the country's intelligence services have aided such groups. Pakistan denies the charge and accuses India of fomenting unrest in its own southwestern Balochistan province.

The military skirmish followed a suicide attack in the Indian-administered Kashmir town of Pulwama, which killed more than 40 Indian security forces personnel. Both India and Pakistan claim the mountainous Kashmir territory in full, but administer separate parts of it. They have fought two of their three wars over Kashmir.

Twitter exchanges
Khan had congratulated Modi on his election win shortly after results were announced last month, saying in a Twitter post that he "look[ed] forward to working with him for peace, progress and prosperity."

Imran Khan Tweet
I congratulate Prime Minister Modi on the electoral victory of BJP and allies. Look forward to working with him for peace, progress and prosperity in South Asia
He followed up with a formal letter sent earlier this month, local media reported, in which he renewed Pakistan's offer to resume talks.

Modi responded to Khan's congratulatory tweet by saying he had "always given primacy to peace and development in our region".
Modi Tweet
Thank you PM @ImranKhanPTI.

I warmly express my gratitude for your good wishes. I have always given primacy to peace and development in our region. https://twitter.com/ImranKhanPTI/status/1131526476828893184 …
Thursday's messaged echoed that sentiment, hinting at a possible resumption of dialogue without committing to it.

"For [normal relations], it is important to build an environment of trust, free of terror, violence and hostility," Modi said in his letter, the Indian foreign ministry said.

For his part, Jaishankar, the Indian foreign minister, "emphasised the need for an 'atmosphere free from the shadow of terror and violence'," the statement said.

In May, Pakistani Foreign Minister Shah Mehmood Qureshi held informal talks with his then-counterpart, Sushma Swaraj, on the sidelines of a Shanghai Cooperation Organisation (SCO) meeting in the Kyrgyz capital Bishkek.

Khan and Modi shook hands at a meeting of the SCO last week, Pakistan's foreign minister said.