In a letter to the UN, the US said that it is ready to negotiate with Iran.
Iran has retaliated by firing missiles at air bases housing US forces in Iraq causing no casualties. It also told the UN it was an act of self-defence.
General Soleimani was widely held as being Iran's second most senior official.
As head of the Revolutionary Guards' elite Quds Force, he was an architect of Iranian policy in the region.
What do the letters say?
In a letter to the UN Security Council, US Ambassador to the UN Kelly Craft said the US was ready to negotiate "with the goal of preventing further endangerment of international peace and security or escalation by the Iran".
The US would take additional action "as necessary" in the Middle East to protect its personnel and interests, the letter added.
But Iran's UN Ambassador Majid Takht Ravanchi said the US offer of talks was "unbelievable" while the US continued to enforce harsh economic sanctions on Iran.
Ayatollah Khamenei said that if the US rejoined a landmark nuclear deal it withdrew from in 2018, it could take part in multilateral talks with Iran and the other parties to the deal.