The letter is the latest move to signalling a thaw in ties between the two nuclear-armed neighbors.
What did the letter say?
The letter from Modi arrived on Tuesday, coinciding with Pakistan's Republic Day, Pakistani officials told Reuters news agency and the Associated Press (AP).
"As a neighboring country, India desires cordial relations with the people of Pakistan,'' Modi wrote in the letter, according to the AP.
He added: "For this, an environment of trust, devoid of terror and hostility, is imperative.''
Pakistani newspaper Dawn also reported on the contents of the letter.
The Times of India newspaper reported that the message from Modi "was a routine letter which is sent every year."
What has the reaction been?
Senior Pakistani minister, Asad Umar, praised Modi's letter, calling it a "message of goodwill."
In a post on Twitter, he added that Khan has expressed a desire for peaceful relations between the neighbors "based on mutual respect & [peaceful] coexistence."
Why is this significant?
Modi's letter, should its contents be confirmed, is the latest in a series of statements which hint at possible rapprochement between India and Pakistan.
The two sides are currently holding talks in Delhi about water sharing.
Over the weekend, Modi wished Khan well after the latter was confirmed to be infected with COVID-19.
Last week, the head of Pakistan's powerful army chief called for a peaceful resolution in disputes over the region of Kashmir, as well as peace talks with India.
In a surprise move in February, both sides announced a ceasefire along one of the disputed borders in Kashmir.
India and Pakistan have fought three wars since gaining independence from Britain in 1947 — with two of the conflicts starting over Kashmir.
rs/dj (AP, Reuters)