The offer, made at the start of an international conference aimed at creating a platform for peace talks, adds to a series of signals from both the Western-backed government and the Taliban suggesting a greater willingness to consider dialogue.
Ghani proposed a ceasefire and a release of prisoners as part of a range of options including new elections, involving the terrorists, and a constitutional review as part of a pact with the Taliban to end a conflict that last year alone killed or wounded more than 10,000 Afghan civilians.
"We are making this offer without preconditions in order to lead to a peace agreement," Ghani said in opening remarks to the conference attended by officials from around 25 countries involved in the so-called Kabul Process.
"The Taliban are expected to give input to the peace-making process, the goal of which is to draw the Taliban, as an organisation, to peace talks," he said, adding that he would not "pre-judge" any group seeking peace.
The comments, a month after a suicide attack in central Kabul killed around 100 people, represented a change in tone for Ghani, who has regularly called the Taliban "terrorists" and "rebels" although he has also offered to talk with parts of the movement that accepted peace.
The United Nations mission in Afghanistan welcomed the offer and said it "strongly supports the vision for peace through intra-Afghan dialogue".
The Taliban, fighting to restore Islamic rule after their 2001 defeat by US-led troops, have offered to begin talks with the United States but have so far refused direct talks with Kabul. It was unclear whether they would be prepared to shift their stance, despite growing international pressure.
However Ghani, who recently helped launch the latest stage in a major regional gas pipeline from Turkmenistan, said the momentum for peace was building from neighbouring countries that increasingly saw the necessity of a stable Afghanistan.
"The Taliban show awareness of these contextual shifts and seem to be engaged in a debate on the implications of acts of violence for their future," he said.
Ghani said a framework for peace negotiations should be created with the Taliban recognised as a legitimate group, with their own political office to handle negotiations in Kabul or another agreed location.
Taliban officials have acknowledged that they have faced pressure from friendly countries to accept talks and said their recent offers to talk to the United States reflected concern that they could be seen to be standing in the way of peace.
There was no immediate response to Ghani's offer although one Taliban official, speaking on condition of anonymity, said it was being studied by senior Taliban leaders.
Ghani said the process would be accompanied by coordinated diplomatic support including a global effort to persuade neighbouring Pakistan, which Kabul has regularly accused of aiding the Taliban, of the advantages of a stable Afghanistan.
He renewed an offer of talks with Pakistan, which rejects the accusations and points to the thousands of its citizens who have been killed by terrorist groups over the years.
In return for Ghani's offer, the Taliban would have to recognise the Afghan government and respect the rule of law, including the rights of women, one of the priorities for Afghanistan's international partners.
In addition, Taliban prisoners could be released and their names removed from international blacklists, while security arrangements could be made for Taliban agreeing to join a process of reconciliation. Former fighters and refugees could be reintegrated and provided with jobs.
The United States last year stepped up its military assistance to Afghanistan, notably through a sharp increase in air strikes, with the aim of breaking a stalemate with the insurgents and forcing them to the negotiating table.
While the US military says the strategy has hit the Taliban hard, they still control or contest much of the country and continue to inflict severe casualties on Afghan forces.
They also claimed responsibility for two major attacks in Kabul last month that killed or wounded hundreds of civilians.