The wall outside the Iranian consulate in Herat caused traffic congestion and turmoil for six long years. Tehran took down the wall only after it received an unequal bargain for land in Kabul.
About 1,300 Afghans also condemned Iranian and Russian interference in their country's peace talks with the Taliban, citing the group's recent visits to Tehran and Moscow.
The breakthrough, however, comes after a surge of violence in Afghanistan in recent weeks.
Aid will be contingent on the preservation of democracy, rule of law and human rights in the ongoing intra-Afghan peace talks.
Both sides now have resolved several disputed issues, opening the path for talks to advance, said an Afghan official close to negotiators in Doha.
The visit is Khan's first to Kabul since becoming prime minister in August 2018.
Rahmatullah Andar, a spokesman for the National Security Council (NSC) and a former Taliban commander, is a prime example.
The continuation of violence, especially against educational institutions, is unacceptable and contrary to Islam, scholars say.
'We want a system where all Afghans can participate,' says one religious scholar.
A car bomb Sunday exploded near a police headquarters in Ghor Province, leaving at least 16 people dead and 154 wounded, including women and children. Locals blamed the Taliban.