The US killed General Soleimani, who oversaw the Revolutionary Guard Corps's expeditionary Quds Force, and others in the January attack near Baghdad International Airport.
Iran's charges against Trump and others include "murder" and "terrorist acts", charges which carry a maximum penalty of death under Iran's criminal code.
According to reports, Trump is one of 36 people who had warrants issued for their arrest.
Alqasimehr said Interpol was asked to put out a "red notice" on Trump and the other defendants.
The prosecutor general explained that U.S. President Donald Trump is at the top of the list, and he'll be facing prosecution even after his term as president.
Interpol said in a statement that its constitution forbade it to undertake "any intervention or activities of a political, military, religious or racial character".
Under a Red Corner Notice, authorities in the country where the accused are present can make arrests on behalf of the country that requested them.
Interpol "would not consider requests of this nature", it said. "At the top of the list is U.S. president Donald Trump", he added. "It is a propaganda stunt that no-one takes seriously".
Interpol doesn't get involved in political arrest requests.
"This has nothing to do with national security, global peace or promoting stability", Hook said.
In response, the US special representative for Iran, Brian Hook said Tehran was carrying out "a propaganda stunt that no one takes seriously".
Iran retaliated by firing a volley of ballistic missiles at U.S. troops stationed in Iraq, but Trump opted against responding militarily.