The US announced earlier Friday that it had killed the powerful general in a strike on Baghdad's international airport
The commander helped direct wars in Iraq, Syria, Lebanon and Yemen, and he became the face of Iran's efforts to build a regional bloc of Shiite power
The strike also killed the deputy chief of Iraq's powerful Hashed al-Shaabi paramilitary force.
"Following the martyrdom of the glorious general haj Qasem Soleimani, I name Brigadier General Esmail Qaani as the commander of the Quds Force"
Foreign Minister Mohammad Javad Zarif denounced the attack as a "dangerous escalation"
"Wow - the price of killing and injuring Americans has just gone up drastically," Senator Lindsey Graham, a close confidant of Trump, wrote on Twitter.
We will take revenge from all those involved and responsible for his assassination, Amir Hatami said
Trump spoke with Abdel Mahdi earlier by telephone, stressing the need to protect Americans and US facilities in Iraq, the White House said.
Iran again denied involvement in the Sept. 14 raids, which hit the world's biggest crude oil processing facility and initially knocked out half of Saudi output
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Pompeo said on Thursday in an interview with Bloomberg that he would "happily" go to Tehran and willingly appear on Iranian television
Trump asserted that the US reserved the right to defend its personnel, facilities and interests
The stand-off, coupled with a weak dollar as the Federal Reserve flags an interest rate cut, has helped push gold prices to six-year highs above $1,400
Two officials told The Associated Press on Saturday that the strikes were conducted with approval from Trump
The sanctions move, announced on Twitter with no additional detail, came as Trump spent the day at the Camp David presidential retreat having meetings and phone calls
Iran warned the United States on Saturday that any aggression against the Islamic republic would have serious consequences
The security premium built into oil prices could rise further as tensions between the US and Iran heat up
American and Iranian officials are disputing the circumstances of the incident
The BAMS-D drone was downed by an Iranian surface-to-air missile system while flying in international airspace over the Strait of Hormuz