"What's going on between Pakistan and India if we can help, we certainly will be willing to. We have been watching it very closely and it's an honour to be here with my friend," he said.
"The Pakistan-India conflict is a very big issue for us in Pakistan and we expect the US to always play its part in deescalating the tensions, because no other country can," Khan said.
President Trump has repeatedly offered to mediate following India's August 5 decision to revoke the special status to Jammu and Kashmir and bifurcate the state into two Union Territories, evoking strong reaction from Pakistan which has been trying to internationalise the Kashmir issue.
New Delhi has defended the move, saying Jammu and Kashmir is an integral part of India and the issue was strictly internal to the country, and the special status provisions only gave rise to terrorism in Jammu and Kashmir.
"The country took the decision of abrogation of Article 370, which had only given separatism and terrorism to that state," Prime Minister Narendra Modi said at a function in October last year.
This is the third meeting between Trump and Khan since Pakistan premier assumed office in 2018 and it came against the backdrop of Pakistan Foreign Minister Shah Mehmood Qureshi's recent trip to the US, amid reports that the US and Afghan Taliban were close to striking a peace deal.
"There are issues we want to talk about. The main issue is Afghanistan because it concerns the US and Pakistan. Fortunately, we are on the same page. Both of us are interested in peace there and an orderly transition in Afghanistan with talks with Taliban and the government," Khan said.
When a reporter asked Trump if he would visit Pakistan considering he was already set to visit India, the US president said he was meeting the Pakistan premier in Davos.
"Well, we're visiting right now. So we don't really have to. I wanted to say that from a relationship standpoint, we got a great relationship. From the standpoint our two countries, we're getting along very well. I would say we've never been closer with Pakistan the way we're right now. And this is a big statement," Trump said.
Khan left for Switzerland to attend the World Economic Forum and meet the world leaders, including President Trump, on the sidelines of the annual event which kicked off at the ski resort town of Davos on Tuesday.
The four-day summit marks the 50th anniversary of the forum.
A total of 53 heads of State are on the guest list. Nearly 3,000 participants from 118 countries are expected to attend the event during which political leaders, business executives, heads of international organisations and civil society representatives are set to deliberate on contemporary economic, geopolitical, social and environmental issues.