"Let this serve as a WARNING that if Iran strikes any Americans, or American assets, we have targeted 52 Iranian sites (representing the 52 American hostages taken by Iran many years ago), some at a very high level & important to Iran & the Iranian culture, and those targets, and Iran itself, WILL BE HIT VERY FAST AND VERY HARD".
The American attack, in turn, came as retaliation for a rocket strike that killed a USA contractor in Kirkuk, Iraq, some days earlier.
U.S. Democratic lawmakers have demanded more information about the airstrike, which was carried out without consulting Congress, and before Trump's expected impeachment trial in the Senated later this month.
Iran has promised "harsh revenge".
In a sabre-rattling tweet, Trump said: "If they attack again, which I would strongly advise them not to do, we will hit them harder than they have ever been hit before!"
"Death to America", they chanted at a mass gathering in the streets of the southwestern city, where Soleimani's remains arrived from Iraq before dawn, according to semi-official news agency ISNA. After that war, Soleimani joined the Guard's newly formed Quds, or Jersualem, Force, an expeditionary force that works with Iranian proxy forces in countries like Iraq, Lebanon and Yemen.
Soleimani was the architect of Iran's Middle East operations.
Al-Istrabadi said that the "red line for the U.S." was crossed when an American contractor was killed last week in an attack that also injured Iraqi servicemen.
Though it's unclear how or when Iran may respond, any retaliation was likely to come after three days of mourning declared in both Iran and Iraq.
U.S. law requires notification within 48 hours of the introduction of American forces into an armed conflict or a situation that could lead to war.
North Atlantic Treaty Organisation has suspended Canadian-led training of Iraqi forces in the wake of the airstrike, and Defence Minister Harjit Sajjan said Canada is monitoring the security environment and taking necessary precautions.
Soleimani was killed in a United States drone strike Friday near Baghdad global airport that shocked the Islamic republic.
"We ask security forces in the country to get at least 1,000 meters away from U.S. bases starting on Sunday at 5:00pm (1400 GMT)", said the group. The Iraqi military confirmed the missile attacks in Baghdad and on al-Balad and said there were no casualties.
Will killing Qassem Soleimani help Trump get reelected? In the first hints of a possible retaliatory response, two mortar rounds hit an area near the U.S. embassy in Baghdad on Saturday, security sources told AFP.
Also Saturday, NATO temporarily suspended all training activities in Iraq due to safety concerns, Canadian Defense Minister Harjit Sajjan said.
Among the mourners in Iraq included many militiamen in uniform for whom they were heroes. Britain and France have warned their citizens to avoid or strictly limit travel in Iraq.
During a phone conversation at the initiative of the Iranian side, Lavrov expressed his condolences over the killing of Soleimani in a US airstrike, the Russian Foreign Ministry said in a statement.