According to Indian media, Modi wrote this to Khan in response to his congratulatory message earlier this month on him becoming the Prime Minister again.
External Affairs Minister S. Jaishankar also conveyed similar views to his counterpart Shah Mehmood Qureshi in response to his congratulatory message.
"As per the established diplomatic practice, the Prime Minister and the External Affairs Ministry have responded to congratulatory messages received from their counterparts in Pakistan," a Ministry spokesperson said.
"In their messages, they have highlighted that India seeks normal and cooperative relations with neighbors, including Pakistan," the spokesperson added.
The Prime Minister said: "For this, it is important to build an environment of trust, free of terror, violence and hostility."
Jaishankar also emphasized to his counterpart the need for an "atmosphere free from the shadow of terror and violence", the spokesperson said.
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.
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