The US says it is ready to take part in "serious negotiations" with Iran as it insisted the killing of Iranian commander Qassem Soleimani was an act of self-defence.
In a letter to the UN Security Council, the US also vowed to take additional action "as necessary" in the Middle East to protect its personnel and interests.
It comes after US President Donald Trump said Iran "appears to be standing down" from the brink of war after Tehran carried out missile strikes on two Iraqi bases housing US troops.
Meanwhile, the Foreign Secretary Dominic Raab has said the UK is assessing the future of Iran's 2015 nuclear deal due to "acute" non-compliance by Tehran.
On Wednesday, Mr Trump had urged world powers including the UK to follow Washington's lead by abandoning the deal so a new agreement could be reached.
US Ambassador Kelly Craft has told the UN that America stands "ready to engage without pre-conditions in serious negotiations with Iran, with the goal of preventing further endangerment of international peace and security or escalation by the Iranian regime".
She said the death of Major General Qassem Soleimani - as well as US airstrikes in Iraq and Syria on 29 December against an Iran-backed militia group - were "in response to an escalating series of armed attacks in recent months by the Islamic Republic of Iran and Iran-supported militias on US forces and interests in the Middle East".
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The killing of Maj Gen Soleimani in Iraq last Friday was justified under Article 51 of the UN Charter, Ms Craft wrote in the letter, which has been seen by the Reuters news agency.
Under Article 51, countries are required to "immediately report" to the 15-member UN Security Council any measures taken in exercising the right of self-defence.
Iran also justified its action under Article 51 in a separate letter to the UN Security Council on Wednesday.
Iran's UN Ambassador Majid Takht-Ravanchi wrote that the country "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".
Mr Ravanchi wrote: "The operation was precise and targeted military objectives thus leaving no collateral damage to civilians and civilian assets in the area."
Dominic Raab held talks with US Secretary of State Mike Pompeo in Washington on Wednesday night as he called for restraint from both sides.
He also welcomed Mr Trump's calls earlier in the day for a diplomatic resolution, while stressing the need to restrict Iran's nuclear ambitions.
"We made clear we recognise the danger and threat that Iran poses to the region," Mr Raab said.
"We also recognise the US right to set its self-defence (but) at the same time, of course we want to see the tensions de-escalated."
Asked if he was clear about the legality of the US assassinating Maj Gen Soleimani, Mr Raab said: "It's not for us to substitute our judge for the operation decision the US makes, but there is clearly a right of self-defence and through international law."
There were signs that the two sides were stepping back from the brink of a potentially devastating war following Iran's missile barrage which hit bases used by US and British troops in Iraq.
US officials said 15 missiles were fired, with 10 striking the Ain al Asad base 100 miles west of Baghdad, one striking a base in Erbil in northern Iraq's semi-autonomous Kurdish region, and four missing their targets.
No casualties were reported in the attacks, but in an apparent show of determination, Mr Trump insisted the US would impose economic sanctions on Iran that would remain in place until it "changes its behaviour".
The Iranian missile attacks were in response to the US decision to target Maj Gen Soleimani, who was killed in a US drone strike in Baghdad last Friday.