"Those who sort of question the sincerity of the president's invitations, I would just point to the fact that he's now met twice with [North Korean leader] Kim Jong-un", Hook said an event hosted by the Axios media outlet in Washington.
Hook also noted there is much tension in the Middle East and the United States is doing everything it can to de-escalate the situation.
The US president would be happy to sit down with Iran's leadership even though Iran has rejected diplomacy on many occasions, the special representative concluded.
On Sunday, Iranian President Hassan Rouhani said Tehran is ready to hold negotiations with the United States if Washington lifts sanctions and gives up its bullying.
Tensions between the United States and Iran have increased since 2018 when Washington pulled out of the landmark 2015 multilateral nuclear agreement and started unveiling the "toughest ever" sanctions on the Islamic republic.
On the anniversary of Trump's pullout from the nuclear agreement, Iran announced it had partially discontinued its commitments under the accord. Iran also gave the European Union - a signatory of the agreement - 60 days to ensure Iran's interests were protected under the accord.
Iran announced that starting on 7 July, it would begin enriching uranium beyond the 3.67 percent limit outlined in the nuclear agreement and stop the process of repurposing its nuclear reactor in Arak.
The United States was close to undertaking military action against Iran after a US drone was shot down by the Iranian military, but President Donald Trump has repeatedly said he is open for talks with the Iranian leadership without any preconditions.