ISLAMABAD, Pakistan — Pakistan's top diplomat has admitted what the country has long denied: that it supports some members of the Afghan Taliban and gives them shelter.

Sartaj Aziz, Pakistan's Advisor to the Prime Minister on Foreign Affairs, told an audience at the Council for Foreign Relations Tuesday that Pakistan had "some influence" in convincing the militant insurgent group to the negotiating table "because their leadership is in Pakistan."

He said: "I think people who have dealt with this issue recognize that Taliban in the best of times … did not listen to Pakistan always…and now we have some influence on them because their leadership is in Pakistan and they get some medical facilities, their families are here. So we can use those levers to pressurize them to say 'come to the table.'."

Aziz, who was in Washington this week to meet counterpart John Kerry for the latest round of Pakistan-U.S. talks, admitted that Islamabad could not "negotiate on behalf of the Afghan government because we can't offer them what the Afghan government can offer them."

A spokesman for Pakistan's Ministry of Foreign Affairs responded Thursday to Aziz' admission, saying: "You need to see things in their correct perspective. I will not comment on the adviser's statement."

The Pakistan-U.S. 'strategic dialogue' is a series of high level talks aimed at improving cooperation and convincing the Taliban to negotiate an end to its 15 year-old insurgency and America's longest war.