In a letter to the UN, the US justified the killing of Iranian General Qasem Soleimani as an act of self-defence, the BBC reported on Thursday.
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.
Gen. 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.
Iran's Supreme Leader Ali Khamenei described the missile attacks as a "slap in the face" for the US and called for an end to the American presence in the Middle East.
The US strike on Soleimani also killed members of Iran-backed Iraqi militias, who have also vowed revenge.
However, US Vice-President Mike Pence told a leading media outlet that "intelligence" indicated that Iran had asked its allied militias not to attack US targets.
The US House of Representatives has scheduled a vote for Thursday on limiting President Donald Trump's ability to wage war against Iran without specific approval from Congress.
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 Iranian regime".
The killing of Soleimani was justified, the letter argued, under Article 51 of the UN Charter, which requires states to "immediately report" to the Security Council any measures taken in exercising the right of self-defence.
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.
Iran also cited Article 51 as justification for its attack on US bases.
In the Iranian letter, Ravanchi wrote that Tehran "does not seek escalation or war" after exercising its right to self-defence by taking a "measured and proportionate military response targeting an American air base in Iraq".
"The operation was precise and targeted military objectives thus leaving no collateral damage to civil and civilian assets in the area," he wrote.
US President Donald Trump has previously threatened military action against Iran if it were to target US personnel and bases, but he did not announce any military action, saying Iran's attack had caused no casualties.
"No Americans were harmed in last night's attack by the Iranian regime," he said.
"Iran appears to be standing down, which is a good thing for all parties concerned," he added.
The US House of Representatives is expected to vote on Thursday on a resolution to force Trump to halt further military action against Iran unless Congress gives it the all-clear.
"Members of Congress have serious, urgent concerns about the administration's decision to engage in hostilities against Iran and about its lack of strategy moving forward," Nancy Pelosi, speaker of the House, said in a statement.
It was the most direct assault by Iran on the US since the seizing of the US embassy in Tehran in 1979.
A total of 16 missiles were launched from at least three sites in Iran on Wednesday, Defence Secretary Mark Esper said.
At least 11 of them struck the air base in Al Asad, west of Baghdad, and at least one more hit the Irbil base, he said. Several other missiles landed at some distance from the targets.
( With inputs from IANS )