Modi wrote this to Khan in response to his congratulatory message earlier this month on his becoming the Prime Minister again.
External Affairs Ministry spokesperson Raveesh Kumar said at a media briefing here on Thursday that the Prime Minister's letter made no mention about talks and termed as "fake news" the reports appearing in Pakistani media.
"There is no change in the situation or our position...It is an established diplomatic protocol that whenever someone writes to you, you respond. The Prime Minister received letters from several foreign leaders and he responded," Kumar told reporters, adding the June 12 letter to Khan was keeping in with that protocol.
He said Modi wrote to Khan that, "We want normal and cooperative relations" and for that Pakistan needs to "create an atmosphere which is free of terror and violence".
When asked to comment on reports in Pakistani media which claimed that the Indian Prime Minister had expressed readiness to hold talks, the MEA spokesperson termed it as "distortion" and "fake news peddling".
He said it was just "simple, straight forward" letter and there was no mention of talks.
To another question, Kumar said, "There is no change in our position. We have said Pakistan has to take action against terrorism, which is irreversible."
He maintained that there can be no talks with Pakistan, "unless we are convinced that action (against terror) has been taken on the ground and not superficial action like has been taken recently. We will not be fooled."
Khan had written a letter to Modi earlier this month, congratulating him on becoming the Prime Minister and saying that there should be dialogue to resolve the outstanding issues between the two countries.
Pakistan Foreign Minister Shah Mehmood Qureshi also had written a letter to S. Jaishankar after he took over as External Affairs Minister.
"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, Kumar said.
"In their messages, they have highlighted that India seeks normal and cooperative relations with neighbours, 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," Kumar added.
The spokesperson said Modi, in his letter, also mentioned about the proposed Kartarpur corridor and sought its early operationalisation, since it has been a long-pending demand of Sikh pilgrims.
"We have held three technical-level discussions (on the proposed corridor). We have made some queries to Pakistan and are waiting for a response," he said, adding the Indian government is committed to this corridor.
( With inputs from IANS )