Maj Gen Soleimani was killed on Friday morning in the strike ordered by US President Donald Trump on Baghdad's international airport, in a dramatic escalation of tensions between the two countries.
"COAS received telephone call from US Secretary of State Mike Pompeo. Regional situation including possible implications of recent escalation in Middle East was discussed," Dawn news reported citing the Inter-Services Public Relations (ISPR) as saying in a tweet on Friday night.
"COAS emphasised need for maximum restraint and constructive engagement by all concerned to de-escalate the situation in broader interest of peace and stability.
"COAS also reiterated the need for maintaining focus on success of Afghan Peace Process," the ISPR added.
Besides speaking to Bajwa, Pompeo also made calls to German Minister for Foreign Affairs Heiko Maas, French Foreign Minister Jean-Yves Le Drian, and Afghan President Ashraf Ghani.
Following the development, the Pakistan Foreign Office earlier on Friday expressed "deep concern" over the tensions, urging all sides to exercise restraint, said Dawn news.
"Pakistan has viewed with deep concern the recent developments in the Middle East, which seriously threaten peace and stability in the region," it said.
The Foreign Office urged all parties involved to "exercise maximum restraint, engage constructively to de-escalate the situation, and resolve issues through diplomatic means, in accordance with UN Charter and international law".
( With inputs from IANS )