Indian Foreign Secretary Subrahmanyam Jaishankar was willing to attend talks on the invitation of his Pakistani counterpart, the sources said, adding that they should focus on the situation in Kashmir.
The olive branch comes after 40 days of violent protests in Kashmir that were sparked by the killing by security forces of a field commander of militant group.
At least 64 people have died and thousands been injured in clashes with security forces that have been denounced by Pakistan, which also claims the right to rule Jammu & Kashmir in a territorial dispute that dates back to partition in 1947.
In the latest clash on Wednesday, militants killed three members of the security forces when they ambushed an army convoy and then fired on a police jeep that came to the scene.
The sources made it clear, however, that India “rejects in their entirety the self-serving allegations regarding the situation in J&K, which is an integral part of India.”
Prime Minister Narendra Modi ratcheted up tensions in his annual Independence Day speech on Monday, accusing Pakistan of glorifying terrorism.
And, in a tit-for-tat escalation in the war of words, Pakistan accuses India of meddling in Pakistani trouble spots, in particular of helping separatists fighting the Pakistani state in resource-rich Balochistan.
Both sides deny the accusations.