Graham, in tweets on late Wednesday, said that he spoke to Pakistan's Foreign Minister Shah Mahmood Qureshi on the "growing crisis" in Kashmir and expressed hope that the "Trump administration would help de-escalate the current crisis".
"Just spoke with the Pakistani Foreign Minister about the growing crisis in Kashmir. India's decision to change the status quo must be addressed before it leads to a further escalation of tensions.
"Hope the Trump administration will provide assistance to both Pakistan and India to find a way to de-escalate the current crisis. The last thing the region and the world needs is further military confrontations between India and Pakistan over Kashmir," he tweeted.
Graham's remarks came after Pakistan expelled the Indian High Commissioner and downgraded its diplomatic ties with New Delhi, among other steps, in response to New Delhi's scrapping of special status to Jammu and Kashmir.
President Donald Trump, whose earlier offered to mediate on the Kashmir conflict, is yet to comment on the developments in the region.
In a July 22 statement, Trump had said that Indian Prime Minister Narendra Modi had asked him to mediate on the Kashmir dispute.
Although India denied ever asking him to do so, the US President reiterated his stance last week, saying he's willing to help if both countries ask him to.
Pakistan Prime Minister Imran Khan had that time said he was "surprised" by India's reaction to Trump's offer of mediation to bring Islamabad and New Delhi to dialogue table for resolving Kashmir conflict.
( With inputs from IANS )