Sharif made the request when Obama telephoned him, informing about his forthcoming India visit and discussing bilateral ties and the regional situation.
"The Prime Minister also urged President Obama to take up the cause of Kashmir with the Indian leadership, as its early resolution would bring enduring peace, stability and economic cooperation to Asia," said a Pakistan Prime Minister's Office statement on the discussions between the two leaders.
It said that President Obama informed Sharif of his forthcoming visit to India in January to attend India's republic Day Parade as the Chief Guest.
During the call, Sharif recalled an invitation he extended to Obama last year in Washington and conveyed the expectation of the people of Pakistan to welcome US President to the country some time in the future.
"The President also assured the Prime Minister that he would undertake a visit to Pakistan at an early date, as soon as the situation normalises in the country," the Prime Minister's Office statement said.
During the call, Sharif also referred to his visit to India earlier this year to take relations forward.
Sharif alleged that India subsequently took "unfortunate steps, including cancellation of Foreign Secretary-level talks" and "firing across the LoC resulting in civilian casualties" which showed that "India was averse to normalisation of relations with Pakistan."
Sharif said Pakistan "remains open to the resumption of bilateral dialogue, the onus is on India to create a conducive environment in this regard."
"President Obama expressed his understanding for our position," the statement said.
The two leaders also discussed the regional situation.
The Prime Minister referred to the improvement of Pakistan-Afghanistan relations as manifest in President Ashraf Ghani's recent visit to Islamabad.
President Obama appreciated Prime Minister Sharif's efforts in this regard and called it pivotal for the peace and stability in the region, the statement said.
Sharif recalled his warm and friendly meeting with US President in Washington in October last year and their subsequent interaction at the Nuclear Security Summit in The Hague in March this year, it said.
Later, the White House also confirmed that Obama had called Sharif. "I can confirm that the President did speak with Prime Minister Sharif," Mark Stroh, spokesman of the National Security Council, said.