The US special envoy for Afghanistan visited Kabul on Sunday for the first time since President Donald Trump called off talks with the Taliban in September.
Afghan officials said Zalmay Khalilzad met President Ashraf Ghani to brief him on his continuing efforts to reach a peace agreement with the Afghan insurgents.
"The aim of his visit is clear, to report to President Ghani on his recent visits and meetings in some countries regarding the Afghan peace process," an official in Mr Ghani's office said.
A presidential statement issued after the meeting said Mr Ghani and Mr Khalilzad “emphasised lasting peace, a reduction of violence, and a ceasefire for the intra-Afghan talks”.
They also discussed transparency in last month's presidential election, and the need for the Independent Election Commission to maintain independence and impartiality, it said.
Mr Ghani and Afghanistan's Chief Executive Abdullah Abdullah were the leading candidates in the election. The results were expected on October 19 but the election commission delayed the announcement, citing technical issues and the need to ensure transparency.
Mr Khalilzad also held talks with Mr Abdullah on Sunday.
His visit to Kabul follows a series of low-key meetings he has held recently, including with the Taliban this month in neighbouring Pakistan, with the European Union and United Nations, and with China, Pakistan and Russia in Moscow on Friday.
Mr Trump suspended nearly a year of direct talks with the Taliban after a bomb attack by the insurgents in Kabul on September 5 that killed at least a dozen people including a US soldier.
Comments by Taliban and US officials at the time suggested a peace deal was imminent after nearly a year of talks between Mr Khalilzad and Taliban representatives in the Qatari capital Doha, where the insurgents have a political office.
The deal involved the withdrawal of US troops from Afghanistan in exchange for Taliban security guarantees and was expected to go ahead despite concerns from some US security officials and the Afghan government that it could bring more conflict and a resurgence of extremist militant factions.
The Taliban refused to talk directly to Mr Ghani's government, which it dismisses as a US puppet.
Despite calling off the talks, Mr Trump remains keen on reaching a deal with the Afghan insurgents, which would end America's longest war and allow him to make good on his election promise to bring US troops home from overseas engagements. The United States has about 12,000 troops in Afghanistan.