Saudi crown prince's brother discusses Iran crisis in Washington
Saudi Arabia has been at the helm of an international coalition war against Yemen's Houthi rebels since 2015, but has recently come into difficulties with coalition partner the UAE over its support of southern Yemeni separatists.
Pompeo reitirated the US' desire for a negotiated solution between the UAE-backed Southern Transitional Council (STC) and the Saudi-backed government, the State Department said.
Prince Khalid, a former ambassador to the US, and Pompeo agreed that dialogue was the "only way to achieve a stable, unified, and prosperous Yemen", according to a State Department spokesperson.
"Very important for the unity, stability, and prosperity of Yemen that the Yemeni government and STC resolve their dispute," Pompeo said in a tweet.
Yemeni government forces in Aden have been bombed by the UAE, local reports said on Thursday, adding that up to 40 people had been killed in the strikes targeting the internationally recognised and Saudi-backed government.
The Saudi Foreign Ministry also said the two discussed increasing tensions in the Gulf region over Iran's "hostile activities".
Tensions over that move have gradually risen, with Iran seizing tankers in the Gulf in recent months and Britain detaining an Iranian tanker off of Gibraltar.
Saudi Arabia, a longtime regional rival of the Islamic republic, has also blamed Iran for a series of attacks on tankers and other oil installations in the Gulf this year.
The State Department said on Wednesday that the Saudi defence official and the Secretary of State discussed "stronger maritime security" in the Gulf in response to the tanker detentions.
The US has been seeking to form a coalition to guarantee freedom of navigation in the Gulf.
Britain, which already has warships on protection duty in the Gulf after a UK-flagged tanker was seized by Iranian Revolutionary Guards, has said it will join the planned operation.
But other European countries have declined to join, for fear of harming European efforts to rescue a 2015 treaty with Iran over its nuclear programme.