Senior Afghan officials will travel to Pakistan soon to speak to former Taliban deputy commander following a breakthrough in negotiations during a London summit, the Afghan presidential palace said.
Mullah Abdul Ghani Baradar is a long-time friend of reclusive Taliban leader Mullah Mohammad Omar and is seen by some in Afghanistan as the key to restarting peace talks.
Baradar was the second-in-command of the Taliban until his arrest in Pakistan in 2010. He was released from prison last month, but remains in Pakistan.
The decision was made on Tuesday at a meeting attended by Karzai, the British prime minister David Cameron and his Pakistani counterpart, Nawaz Sharif.
"The three leaders spoke about the role of Pakistan in the peace process of Afghanistan and all three agreed that a delegation of the High Peace Council of Afghanistan make a trip to Pakistan and meet with Mullah Baradar," the announcement said on Wednesday.
It remains unclear, however, if Baradar will agree to meet the Afghan delegation.
The Taliban have so far refused to talk directly to Karzai, his government or its representatives.
Attempts to open talks in June failed after Karzai accused the fighters of setting up a government-in-exile in Qatar.
The Taliban refused to remove their flag and a sign identifying the movement as the Islamic Emirate of Afghanistan.
The Qatar office has since closed.
Hidden in a 'safe house'
Baradar's whereabouts have not been known since his release. He is believed to be in a Pakistani government "safe house".
Karzai hopes that Baradar can help kick-start negotiations to end the 12-year war.
Along with Taliban leader Mullah Mohammed Omar, Baradar was a founding member of the Islamic armed movement.
One senior Taliban official said recently that Baradar is still under house arrest in Pakistan and is not allowed to see his family until he agrees to meet the High Peace Council, which was set up by Karzai to negotiate with the religious govement.
He said Baradar met Taliban members while in custody and assured them that he would not defy Mullah Omar's orders forbidding direct talks with the Afghan government.
During the London meeting, the announcement said that Sharif accepted an invitation from Karzai to visit Kabul in coming weeks and that their interior ministers will also meet to discuss border security.