Afghan government negotiators expressed cautious optimism for progress on issues including ceasefires as peace talks with the Taliban were under way in Doha on Sunday.
At an opening ceremony in Doha on Saturday, the Afghan government and allies including the US called for a ceasefire.
But the Taliban, who have fought a guerrilla campaign against both since they were forced from power in 2001, did not mention a truce as they came to the negotiating table.
The head of the peace process for the Afghan government, Dr Abdullah Abdullah, suggested the Taliban could offer a ceasefire in exchange for the release of more of their jailed fighters.
"This could be one of their ideas or one of their demands," said Dr Abdullah, who left Doha for Kabul on Sunday night as scheduled.
He said the talks should continue in the "spirit of moving towards peace".
"There should first be a significant reduction in violence, then humanitarian ceasefires, and then a nationwide and permanent ceasefire," Dr Abdullah said.
The Afghan government side said on Twitter that "the first meeting between the contact groups of the two negotiation teams took place".
Schedules for the talks and a code of conduct were discussed, the tweet said.
Taliban spokesman Mohammad Naeem also confirmed the start of technical talks.
Negotiations will be arduous and messy, delegates warned, as bloodshed continued to grip Afghanistan.
"We will undoubtedly encounter many challenges in the talks over the coming days, weeks and months," US Secretary of State Mike Pompeo said Sunday in Doha, as he called for the warring sides to "seize this opportunity" for peace.
Almost two decades since the US-led invasion that toppled the Taliban, dozens of people are killed each day and the country's economy has been shattered, pushing millions into poverty.
The Taliban have long worried that reducing conflict could lessen their influence.
Officials said six police were killed in a Taliban attack in Kunduz overnight, while five officers died in Kapisa province.
A roadside mine blast in the capital wounded two civilians, and there was another explosion in Kabul district but no casualties.
Dr Abdullah, chairman of Afghanistan's High Council for National Reconciliation, called the surge in violence a "miscalculation".
"We are fired up and ready to end this fight," said Nader Naderi, an Afghan government negotiator.
At the opening event, Taliban co-founder Abdul Ghani Baradar repeated the insurgents' message that Afghanistan should be run under Islamic law, which is expected to be a sticking point.
Mr Baradar and Mr Abdullah met Qatari Emir Sheikh Tamim on Sunday to discuss the process.
A comprehensive peace deal could take years and would depend on the willingness of both sides to adapt their competing visions for Afghanistan and the extent to which they can agree to share power.
President Ashraf Ghani's government wants to maintain a western-backed constitutional republic that has enshrined many rights, including greater freedom for women.
Four of the 21 people on the Kabul negotiating team are women.
The Taliban, who stripped women of all basic freedom while in power from 1996 to 2001, had no female negotiators.
Ashley Jackson, a researcher at the Overseas Development Institute said she "anticipated internal differences but (the Taliban) are decision-makers, which cannot be said for the Afghan government side".
Mr Ghani called for "a lasting and dignified peace" that preserved "the achievements of the past 19 years".
Government negotiator Habiba Sarabi said the start of talks had been "very positive".
Dr Abdullah said the process "could be the start of history made in the coming future, and hopefully sooner rather than later".
Experts have suggested the sides might discuss the prospect of an interim or coalition government including all Afghan factions.
But Sultan Barakat, director of the Centre for Conflict and Humanitarian Studies at the Doha Institute, said it was too early for such talk.
"There are a number of issues that need to be addressed before we go into that detail of what kind of government," he told Al Jazeera TV, which is based in Doha.
The US-backed negotiations come six months later than planned because of disagreements over a controversial prisoner swap agreed to in February.
Under the terms of a troop-withdrawal deal between the US and the Taliban, 5,000 insurgent prisoners have already been released in exchange for 1,000 government forces.