Agree to reduce operations to facilitate withdrawal of forces from Afghanistan.
If an agreement is reached, the move could revive hopes for a long-term solution to the conflict in Afghanistan.
Taliban say they handed cease-fire offer to US peace envoy.
Karzai is in New Delhi to participate in the government sponsored Raisina Dialogue.
The denial comes after reports emerged of a potential deal that would see a reduction in fighting after 18 years of war.
A list of about 5,000 Taliban prisoners has been given to the Americans.
It provides a window during which a peace agreement with the United States can be signed.
Taliban spokesman Zabihullah Mujahid in a statement sent to media claims responsibility for the attack.
Statement says Khalilzad and Pakistani leaders and officials talked about a successful conclusion of intra-Afghan talks.
The explosion happened in the volatile district of Jaghatu in Ghazni province.
US special envoy Khalilzad discusses reconciliation process with Qureshi, Gen Bajwa.
Visit planned after signals kingdom is not happy with Imran’s decision to attend Kuala Lumpur summit
A damning new report shows the extent to which America tried to cover up its failures in Afghanistan.
The Asia Foundation survey for 2019 includes 17,812 men and women 18 years of age and older from throughout Afghanistan.
"Pakistan encourages all parties to the conflict to engage constructively as a shared responsibility," says FO.
Zalmay Khalilzad arrived in Kabul to meet President Ashraf Ghani, a senior Afghan official says.
Statement comes after US president's lightening visit to Afghanistan.
Before taking the secret flight to Afghanistan, Trump had been expected to spend Thanksgiving in Florida.
This is Trump's first visit to Afghanistan since becoming president.
"You know we’re pulling way down in Afghanistan. We’re working on an agreement now with the Taliban," says Trump.
Taliban freed US and Australian hostages in a prisoner swap: Afghan officials.
Rula Ghani also emphasises the need to negotiate a durable peace accord.
Washington believes that "a reduction in violence is necessary to bring about a lasting peace," says statement.
SIGAR report also reviews efforts to revive the Afghan peace process, which seeks to end the 18-year-old war.
“Our suggestion is for a one-month ceasefire, followed by negotiations,” says National Security Advisor Hamdullah Mohib.
The Taliban last week said that China invited a delegation to talks in Beijing.
Khalilzad is in Islamabad for the second time in a month.
It is hoped the quadrilateral process is carried forward so that talks between the US and Taliban resume.
Spokesperson of Afghan president's office says Khalilzad informed Ghani of his "recent activities".
The Taliban leaders refuse to talk to Ghani's government, denouncing it as a US puppet.