The US would argue that Soleimani was responsible for unprovoked attacks on American forces in Iraq. Those forces were there at the request of the current Iraqi government.

Soleimani was a man whom Washington believed already had the blood of many US personnel on his hands. Meanwhile the Quds organisation he headed was seen by the US as a terrorist organisation. So his killing may follow a US legal narrative.

How could Iran respond to Soleimani's death?
Iran's Qasem Soleimani: Why the US had him in its sights

"Pre-emptive self defence is never a legal justification for assassination. Nothing is. The relevant law is the United Nations Charter, which defines self defence as a right to respond to an actual and significant armed attack," she said.

"The use of a drone to kill Iranian Gen Qasem Soleimani in Baghdad was not in response to an armed attack on the United States. Iran has not attacked the sovereign territory of the United States," she said.

"In this case, the United States has not only committed an extrajudicial killing, it has carried out an unlawful attack within Iraq."

The statements above are copied from https://www.bbc.com/news/world-middle-east-50982298 , and are a clear summary of the events. 

With these and other fact relevant to the acts of President Donald Trump, we request that the UN initiate an official investigation into this matter as a war crime. Trump acted without the legal consent of the US Congress, summarily ordering the assassination of a foreign official on the soil of a third nation. He must be held accountable for his actions by the nations of the world.