Qureshi is on the final leg of his tri-state visit aimed at diffusing US-Iran tensions, as instructed by Prime Minister Imran Khan.
Besides the Afghan peace process, Qureshi and Pompeo on Friday also exchanged views on matters pertaining to Pakistan-US bilateral cooperation and regional security situation, reports The News International.
Qureshi, who earlier called on the US to remain engaged in Afghanistan's reconstruction even after withdrawal of its troops, informed the top US diplomat that Pakistan would continue its efforts for political solution to the Afghan conflict.
"Pakistan is fulfilling this joint responsibility for the Afghan peace process with sincerity of intent," he said.
In response, Pompeo appreciated Pakistan's "sincere efforts" for the Afghan reconciliation and peace process and a peaceful neighbourhood.
During the talks, Qureshi also briefed Pompeo about discussions held during his recent visits to Iran and Saudi Arabia.
He said that Pakistan desird peace and stability and was determined to play its role to defuse prevailing tensions in the region, Dawn news reported.
The Minister also underlined the need for strengthening bilateral trade and investment "in order to give a practical shape to Prime Minister Imran Khan and President Donald Trump's vision of comprehensive bilateral Pakistan-US relations".
The US was the last leg of Qureshi's three nation trip after visiting Iran and Saudi Arabia.
( With inputs from IANS )