"We have a common challenge, which is Iran, and I think they all recognize it, and we hope they will resolve their dispute in their own way", said Pompeo.
The two countries have been cooperating in various sectors, including trade and business deals, and they are mainly focusing on fighting terrorism and extremism in the world and the Middle East in particular.
"The US secretary of state's remarks on the presence and role of the Islamic Republic of Iran in certain countries in the region are a repetition of absurd and unfounded accusations", Iran's foreign ministry spokesman Bahram Ghassemi said in a statement Monday. It is an arms dealer to the Houthi rebels in Yemen.
Pompeo succeeded Rex Tillerson, a former chairman of Exxon Mobil who was leading USA efforts to end Qatar's isolation.
Saudi Arabia, the United Arab Emirates, Bahrain and Egypt severed diplomatic and transport links with Qatar on June 5, accusing the country of supporting Sunni extremist groups and Iranian-backed Shiite militants.
He also touched upon the allegation that Iran is meddling in Yemen.
In Riyadh yesterday Mr Pompeo reiterated President Trump's threat to terminate the 2015 nuclear agreement with Iran.
"What is said erroneously with regard to Yemen is false, only aimed at deflecting the attention of the worldwide public opinion from the crimes being committed daily by Saudi Arabia in its aggression against the country", he said. "It is just a worthless claim geared to the perpetuation of Saudi Arabia's warmongering, its aggression against Yemen, and the destructive and destabilising presence of foreign powers in the region".