Speaking at a ceremony in Kabul, marking the 17th anniversary of the ratification of Afghanistan's Constitution, the CEO reiterated that the Taliban can only join the peace talks under the umbrella of the Afghan government.
Taliban sources said that they had demanded that USA authorities release 25,000 prisoners and they would free 3,000, but that US officials were not keen to discuss the exchange at this stage.
In a message sent to Pakistan's Prime Minister Imran Khan, through his special envoy, President of Afghanistan recently appreciated Pakistan's efforts to bring peace in Afghanistan and sought his help to broker direct talks between Afghanistan and Taliban.
Taliban spokesman Zabihullah Mujahid said earlier the two sides were still working on the technical details and were not clear on the agenda for the talks.
The Taliban, Afghanistan's largest armed group which was toppled from power by a US-led invasion in 2001, called off their meeting with the U.S. officials in Saudi Arabia this week following Riyadh's insistence on bringing the Western-backed Afghan government to the table.
When asked about a possible withdrawal of a "significant" number of USA troops from Afghanistan, Zarif said Iran believes the presence of United States forces has not helped security and stability in Afghanistan.
"We would never announce any ceasefire until and unless we achieve major gains on the ground".
The Taliban said Khalilzad would visit the United Arab Emirates, Afghanistan, Pakistan, India and China to continue the discussion.
While denying it made a specific overture to Shamkani, the spokeswoman repeated that Trump is open to a dialog with Iran on "urgent national security issues" and wants Tehran to "make fundamental changes in their destructive behavior".
The U.S. embassy tweet said RAND's work was independent of the U.S. government and did not represent U.S. policy. "But if that leadership of the Afghan state is not recognized and is not given value, then we may face a serious challenge", he added.
"The United States supports the desire of the Afghan people and the global community for a political settlement that ends the 40-year conflict and ensures Afghanistan never again serves as a platform for worldwide terrorism", the statement added.
The document, reviewed by Reuters, suggests that the United States and North Atlantic Treaty Organisation withdraw their military missions in phases over an expected period of 18 months, but the United States may continue providing civilian assistance. Zarif said it was up to Afghans to decide what role the Taliban should have but Afghanistan's neighbours would not want them to be in overall control. It has maintained that any peace process and negotiation on Afghanistan has to be an Afghan-led process.
Majority-Shi'ite Iran has long had close ties to Shi'ites in neighboring Afghanistan whose militias have fought the Taliban's Sunni militants.
The Taliban has consistently rejected requests from regional powers to allow Afghan government officials to take part in peace talks, insisting that the United States is its main adversary in Afghanistan. It has cost Washington almost $1 trillion and killed tens of thousands of people. The Taliban attended landmark peace talks in Moscow last November while Taliban representatives from Afghanistan negotiated with Iranian officials in Tehran in December.
The war was waged by an worldwide coalition led by the United States in the wake of the September 11 terror attacks.