Speaking to reporters before flying out on Sunday, Pompeo said he'll be talking to the two U.S. allies "about how to make sure that we are all strategically aligned" and how to build a global coalition to "push back against the world's largest state sponsor of terror."
At the same time, Pompeo reiterated that the U.S. was prepared to negotiate with Iran with no preconditions to ease tensions in the Persian Gulf.
Tensions spiked last week after Iran downed an unmanned U.S. military aircraft.
President Donald Trump said he backed away from planned strikes against Iran after learning that 150 people would be killed but said military action was still an option.
A top UK diplomat has met with senior officials in Tehran to discuss preventing "escalation and miscalculation" amid heightened tensions between the U.S. and Iran.
On Sunday, the UK Foreign Office quoted Andrew Murrison, the minister of state for the Middle East, as saying his visit was aimed at "open, frank and constructive engagement" with his Iranian counterparts.
He said this included reiterating the UK's assessment that Iran almost certainly bears responsibility for recent attacks on oil tankers in the Gulf of Oman, which Iran denies.
Murrison added that Iran must continue to meet its commitments under a 2015 nuclear deal with world powers that the Trump administration withdrew from a year ago before re-imposing crippling economic sanctions on the country.
Iran's president has accused the United States of fueling tensions in an already volatile region, as the crisis between the two countries escalates.
The official IRNA news agency quoted Sunday Hassan Rouhani as saying the "interventionist military presence" of the U.S. is responsible for the Middle East's problems.
Rouhani also denounced what Iran alleges was the incursion of its airspace by a U.S. military drone, which Tehran shot down on Thursday.
Rouhani said: "We expect international bodies to show proper reaction to the invasion move." His remarks came during a meeting with the president of IPU, or Inter-Parliamentary Union, Gabriela Cuevas, in Tehran.
The U.S. says the drone was flying above international waters near the Persian Gulf.
U.S. National Security Adviser John Bolton says Iran should not "mistake U.S. prudence and discretion for weakness."
Speaking alongside Israeli Prime Minister Benjamin Netanyahu in Jerusalem Sunday, Bolton says no one has granted Iran a "hunting license in the Middle East."
The comments come days after President Donald Trump announced he called off military strikes on Iran after learning approximately 150 Iranians would be killed, saying it would've been out of proportion to the shooting down of an unmanned American surveillance drone by Iran.
Bolton, a longtime Iran hawk, says sanctions will continue against Tehran and that the U.S. reserves the right to attack it at a later point. He emphasized that Trump had only "stopped the strike from going forward at this time.'"
An Iranian military commander warned on Sunday that any conflict with Iran would have uncontrollable consequences across the region and endanger the lives of U.S. forces, as tensions between Washington and Tehran flare after the downing of an American surveillance drone.
The semi-official Fars news agency on Sunday quoted Gen. Gholamali Rashid as saying the Trump administration "should behave in a responsible way to protect the lives of American forces."
Gen. Rashid said if war happens, its scope and duration could not be controlled, and blamed any escalation on "U.S. interventionist policy."
The general oversees and coordinates joint military operations in the Iranian Armed Forces.
Iran said it shot down the U.S. drone on Thursday but elected not to fire on a manned U.S. military aircraft flying in the area at the same time.
U.S. military cyber forces launched a strike against Iranian military computer systems on Thursday as President Donald Trump backed away from plans for a more conventional military strike after learning approximately 150 Iranians would be killed.
Saudi Arabia's state airline Saudia says it is rerouting flight paths to some Asian destinations in order to avoid Iranian airspace amid heightened tensions in the Persian Gulf.
The statement Saturday evening follows the U.S. Federal Aviation Administration's decision to bar U.S.-registered aircraft from operating over parts of the Persian Gulf and the Gulf of Oman, after Iran shot down a U.S. military drone on Thursday.
The airline says it's a precautionary measure for aviation safety, and Saudi-owned Al Arabiya news channel says the airline's decision affects flight routes over the Gulf of Oman and the Strait of Hormuz.
Other regional carriers like Etihad and Emirates on Friday announced they too have changed their flight paths in the Persian Gulf region.