'Now is the time to accelerate efforts to reach a negotiated end to the war in Afghanistan,' a joint statement said.
Pakistan will no longer follow the 'strategic depth' policy with Afghanistan, Pakistani Prime Minister Imran Khan said in Washington.
Khalilzad is set to resume talks with the Taliban in Doha.
Turkmenistan hopes to route electricity and natural gas through Afghanistan to promising markets in South Asia, but peace and stability must be established first.
The Taliban agreed to safeguard the security of public institutions but refused calls for a ceasefire.
About 70 delegates -- comprised of Afghans politicians and the Taliban -- are attending the two-day gathering organised by Germany and Qatar.
The intra-Afghan talks are a fresh attempt to make political headway in ongoing peace talks.
The countries agreed to jointly fight terrorism and push the peace process forward.
Pompeo said he hoped for a peace deal 'before September 1'.
Moscow celebrated 100 years of diplomacy with Kabul by inviting the Taliban -- designated as a terrorist organisation in Russia -- to a celebration and talks on Afghanistan's future.