Abdullah made the remarks while speaking at a TV interview Sunday evening in Tehran.
He arrived in the Iranian capital on Sunday morning at the head of an Afghan delegation to review issues of mutual interest with the Iranian officials.
He said Afghan people know that "we want to settle nationwide peace and security in the country (Afghanistan)."
Grounds are prepared for negotiations, and talks with the other side have started, he added.
That "we're interested in the issue of peace" should be shown in practice, Abdullah stressed.
He hoped that the Afghan people could achieve their ultimate goal of overcoming conflicts because the establishment of peace is their main demand.
Abdullah announced that Afghanistan is ready to hold talks but Taliban has not agreed yet.
He further expressed hope that a favorable outcome could be achieved in this regard, stressing that security during talks is Afghans' minimum demand.
Peace in Afghanistan is of benefit to all countries, said Abdullah, noting that civil war cost Afghanistan a lot; though relative consensus has been taken on the peace project.
As Abdullah underlined, people's fate should be decided only through casting votes freely.
On the peace process, Abdullah said the two sides should reach agreement on a comprehensive package which could be acceptable for all Afghan people.
People are tired of a four-decade war, he said, stressing that if talks fail to bear any fruits, then it means that war will continue; and continuation of war brings more pain for the people of Afghanistan.
In Tehran, Abdullah met with Iranian Foreign Minister Mohammad Javad Zarif on Sunday.
Abdullah's visit to Tehran will last for three days.
In September, Zarif in an interview with Fareed Zakaria- CCN's host and member of Board of Directors of the US Council on Foreign Relations- spoke about peace in Afghanistan and said "Well, Iran has always been a participant in any peace effort, from the Bonn Conference in 2001 where Iran played a leading role in getting the parent government in place in Afghanistan to all regional attempts."
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