Pakistani prime minister Nawaz Sharif added to growing international pressure over US drone killings on Wednesday by calling on Barack Obama to end all strikes in his country.

At the end of a long-awaited US trip designed to smooth growing tensions between the US and Pakistan, Sharif told reporters that he had "emphasised the need to end such strikes", which are estimated to have killed between 2,525 and 3,613 people in Pakistan since 2004.

But a 2,500-word joint statement issued by the White House after the one-on-one meeting in Washington and attributed to the two leaders did not mention drone attacks, referring only to a need to respect "sovereignty and territorial integrity".

It said President Obama also "conveyed appreciation for Pakistan's internal and regional security challenges". Both leaders refused to take questions at the end of their two-hour meeting in the Oval Office.

In prepared remarks, Obama acknowledged that there will "inevitably be some tensions … and some misunderstandings between our two countries" but insisted the US-Pakistan relationship will continue to be a "source of strength".

"It's a challenge," Obama added. "It's not easy."

Pakistani criticism of the US drone program is known to irritate some in Washington defence circles, who believe that many of the attacks are secretly sanctioned or even assisted by officials in Islamabad, and regard the public condemnation as hypocritical.

But the White House is also facing its own charges of double standards after detailed reports published this week by Amnesty International and Human Rights Watch accused the US of violating international law by failing to prevent civilian casualties during the attacks.

Analysts close to the administration say the talks between Pakistan and the US may mark a key moment in the drones program, especially since Obama has already indicated – during a speech in May – that he has a preference in future for capturing terrorist suspects where possible.

"There are always two discussions on drones; one behind closed doors," said Karl Inderfurth, a former assistant US secretary of state for the region now at the Center for Strategic and International Studies.

"The real question is whether there is some private understanding about the need to curb the attacks. The numbers have come down since Obama's speech to the National Defense University in May, but not to zero."

Inderfurth said the real significance of Sharif's visit to Washington was to smooth tensions between the two governments before a bumpy withdrawal of US forces in neighbouring Afghanistan.

"The most important part of the meeting is the fact that they are meeting." he added. "It is important that Obama establishes some kind of rapport, so that when things go bad, as they are likely to, he has a personal relationship with his new interlocutor in Islamabad."

In particular, Washington is keen for Pakistan to do more to encourage Taliban participation in peace talks with the Afghan government.

Speaking after his meeting with Obama, Sharif said: "Let there be no doubt about our commitment for a peaceful and stable Afghanistan. This result remains unwavering."

The joint statement added: "The leaders affirmed their commitment to the Afghan-led and Afghan-owned peace and reconciliation process as the surest way to end violence and bring lasting stability to Afghanistan and the region.

"Acknowledging Pakistan's efforts to support an inclusive reconciliation process in which Afghans determine the future of their country, both Leaders called on the Taliban to join the political process and enter into dialogue with the Afghan government."