Speaking at a peace conference in Kabul, he proposed measures including a ceasefire and prisoner swaps.
In return the Taliban would need to recognise the Afghan government and respect the rule of law.
Previous peace talks offers have not stopped attacks by the Taliban, who have yet to respond to the offer.
A Taliban spokesman told the BBC Afghan service they were waiting for reaction from their leadership.
On Monday the militants said they were prepared to enter direct talks with the US to find a “peaceful solution” to the conflict, but made no mention of negotiating with the government in Kabul.
In the past the Taliban have refused to talk to the Afghan government, a longstanding demand of the US.
Mr Ghani held out the possibility that the Taliban could be removed from international blacklists and eventually recognised as a legitimate political group with their own office, in Kabul or another agreed location.
“The Taliban are expected to give input to the peacemaking process, the goal of which is to draw the Taliban, as an organisation, to peace talks,” he told delegates from 25 countries and organisations involved in the so-called “Kabul Process”.
“A ceasefire should be held, the Taliban should be recognised as a political party and trust-building process should be initiated. Now the decision is in your hands, accept peace… and let’s bring stability to this country.”
Tens of thousands of people – combatants and civilians – have been killed in Afghanistan since US-led troops drove the Taliban from power in 2001.
Under previous initiatives, some former Taliban members have surrendered, but the group has only grown stronger.
The US military stepped up assistance to Afghanistan last year and since then air strikes have increased.