Trip comes at a time when President Donald Trump has sent mixed signals about his intentions in Syria.
He told reporters he plans to talk to allies about "modalities by which we may continue to apply pressure" on Iran, branded by Washington a sponsor of "terrorism".
Pompeo will likely face questions about last month's surprise announcement that US troops would soon leave northeastern Syria, where they help battle remnants of Islamic State of Iraq and the Levant (ISIL, ISIS).
He didn't give a timeline on the pullout. Asked about confusion among allies, he said: "I've actually spoken to them all."
As he was leaving Pompeo told reporters: "The United States is still committed to all the missions that we've signed up for with them over the past two years. This is a coalition that understands that the largest threats - terrorism and the Islamic Republic of Iran - are things that we ought to work on jointly and we will be marshaling all of the resources, theirs and ours, to achieve them."
The secretary of state's trip coincides with that of US National Security Adviser John Bolton who is in Turkey, in part to address the issue of Kurdish fighters in Syria and guarantee their safety after a US withdrawal.
Pompeo will deliver an address on Middle East policy in Egypt, whose military ruler turned president, Abdel Fattah al-Sisi, has been a key partner of Trump.