The Taliban side described the meeting as having produced "very positive signals".
A senior official working with the Afghan president said Khalilzad had briefed Ghani about his meetings with senior ministers and top diplomats in four countries who could play a key role.
The Taliban had reportedly met with United States officials in July after an unprecedented ceasefire in June which fuelled hopes that negotiations could bring an end to fighting after 17 years.
The US media noted that Mr Khalilzad, an Afghanistan-born former US ambassador to Iraq and the United Nations, will have to perform a hard balancing act between the Taliban and the Afghan government.
There was no immediate USA reaction to Saturday's assertions by the insurgents. He traveled to Pakistan, the United Arab Emirates, Saudi Arabia and Qatar before returning to Kabul.
At least 17 soldiers have been killed in Taliban raids on two military posts in western Afghanistan, officials said. The officials, who spoke to the Associated Press on Saturday on condition they not be identified because of the sensitivity of the process, said the meetings were held Friday in the Middle Eastern state of Qatar, where the Taliban maintain a political office. It added that the USA envoy reiterated Washington's support for "Afghan-led and Afghan-owned peace process". It did not mention anything about the US envoy's meeting with the Taliban. "All citizens of Afghanistan must be a part of this reconciliation process", said Khalilzad, according to the embassy statement at the end of his four-nation tour.
But ongoing fighting has raised questions about the viability of the US strategy to end the war, which for the past year has focused on forcing the militants, largely with more air strikes, to the negotiating table.
Taliban leaders will continue to have discussions with the newly appointed USA special envoy for peace in Afghanistan, the group said on Saturday, a move that could accelerate diplomatic engagement between the warring sides. The insurgent group has been calling for direct talks with the US, blaming Washington for starting the Afghan war.
No group immediately claimed responsibility for the Saturday bombing.
The Taliban refuses to engage in direct talks with the Kabul government, dismissing it as "stooges of America".
The Trump administration also held its first talks with the Taliban in Qatar, when Deputy Assistant Secretary Alice Wells met them in Doha in July.