Conflict resolution and economic development in Afghanistan will be some of the main priorities of Uzbekistan's foreign policy in 2019, the president said.
The delegation expressed Afghanistan's desire to work closely with Pakistan on finding a political solution to peace with the Taliban.
Afghan officials have denounced recent statements by the Iranian foreign minister and the ongoing support from Iran to the Taliban.
Khalilzad, who met last month with Taliban representatives in Abu Dhabi, will travel to Afghanistan as well as China, India and Pakistan on his latest trip, which will last through January 21.
Recent peace overtures -- involving the Afghan government, United States, Taliban and other international stakeholders -- have sparked hope among war-weary Afghans.
The government is preparing for 'a face-to-face meeting' with the Taliban, officials say.
A Taliban splinter group deemed the summit 'bogus' while Afghans from all sides rejected Russia's alleged aim to foster peace.
The Iranian consulate in Herat has refused to move its walls over the past three years, preventing the widening of the city's central street and causing traffic headaches for residents.
US envoy Zalmay Khalilzad reportedly met with Taliban representatives in Doha, Qatar, to discuss ending the war in Afghanistan through negotiations, officials say.
The Taliban are spreading conspiracy theories in an attempt to undermine a meeting of religious scholars aimed at finding a solution to the war in Afghanistan.
The consulate will enable co-operation, help develop joint projects and attract investment, officials and business leaders say.
A unified front and stronger relations are necessary to fight terrorism and bring sustainable peace to the region, analysts on both sides of the border say.