On Sunday, Karzai's office said in a statement that the US representative "expressed his optimism about the developments and progress" in the peace process, adding that he hoped an agreement will be reached with the Taliban, reports TOLO News.
This was echoed by former finance minister Omar Zakhilwal, also present in Khalilzad's meeting with Karzai, who in a tweet said he heard "good news" about the peace process:
But Ghani's team, tweeted about the President's separate meeting with the envoy, saying: "Khalilzad stated that there wasn't considerable progress in talks with the Taliban and that he hoped they will achieve a result in this respect."
The development comes after Khalilzad's visit to Islamabad on January 31 during which he met Pakistani officials including Foreign Minister Shah Mehmoud Qureshi, Chief of Army Staff General Qamar Javed Bajwa, and other government officials.
In Kabul, views on peace were divided between the political factions in Afghanistan, reports TOLO News.
Ghani wants a ceasefire ahead of a peace deal between the US and the Taliban, while Chief Executive Abdullah Abdullah's office insists on taking advantage of the current opportunity for peace - which is the Taliban's willingness for a reduction in violence - for a short period.
Gulbuddin Hekmatyar, the leader of Hizb-e-Islami, however, has suggested a four-part group of representatives of President Ghani, Chief Executive Abdullah, Hekmatyar himself, and Karzai to get an outcome from the peace process.
Khalilzad also met Abdullah and emphasized that Washington is firm on reduction in violence with a clear definition and mechanism as a pre-condition for signing a peace deal with the Taliban.
Meanwhile, the High Peace Council is insisting on a quick formation of a negotiating team to move the process forward once the two sides agree on a reduction in violence or a ceasefire.
According to reports, the US is believed to have been pushing the Taliban to immediately start intra-Afghan dialogue once the framework agreement regarding the troop withdrawal is signed.
The Taliban, however, were reluctant to commit to the dialogue as they seek at least a month to start talking to other Afghan groups, including the Kabul administration.
( With inputs from IANS )