Tillerson and his Egyptian counterpart, Sameh Shoukry, cited productive discussions on regional security and the struggle against the Islamic State group, whose Egyptian affiliate, based in the Sinai Peninsula, has struck military and civilian targets across the Arab world's most populous country.
Jordanian leaders were upset when the United States recognised Jerusalem as the capital of Israel and suspended some aid for the Palestinians. Doha denies the charges and says the countries are trying to curtail its sovereignty.
He will visit North Atlantic Treaty Organisation ally Turkey on the tour's final stop where the US diplomat is expected to encounter with hard issues regarding the U.S.'s support for the PKK's Syrian affiliate, the Democratic Union Party (PYD).
But the most contentious stop this week is likely to be in Ankara, where a rising tide of anti-Americanism is spurred on by the government's media mouthpieces who have called the United States an enemy of Turkey.
Speaking of US-Turkish relations, he added: "Look it's hard".More news: Turkey's relations with U.S. at make-or-break point - Mevlut Cavusoglu
It will be "a hard conversation", the official continued, referring to the "very hot" Turkish rhetoric on the subject.
"These are some of our closest partners", a senior State Department official told reporters on the condition of anonymity to preview the trip. The rhetoric is hot. "The Turks are angry, and this is a hard time to do business, but it's our belief that there are still some very fundamental underlying shared interests".
Speaking about the polls due to be held from March 26 to 28, Mr Tillerson told reporters that Washington supports "a transparent credible electoral process".
In Jordan, Tillerson is doing damage control after President Donald Trump's recognition of Jerusalem as Israel's capital and decision to withhold aid money from the United Nations agency assisting Palestinian refugees.
"There's no pulling punches on that", a second senior State Department official said.More news: Winter Olympics opening ceremony sees Intel use record 1218 drones
"These are some of our closest partners but they are also partners with whom we are facing some of the toughest issues that we have to face in the region, whether its terrorism, whether it's the future of U.S. assistance, whether it's the final defeat of ISIS (the Islamic State militant group)".
Sisi is running against a single challenger in the March 26-28 poll after more challenging opponents pulled out, some citing intimidation of supporters and other tactics created to give the incumbent an easy win.
However, Mr Tillerson did not respond to a question on whether the USA would freeze part of its military aid to Egypt if the elections were deemed not credible.
"We have noted our concerns about the reports that Egypt's prosecutor general has launched an investigation into opposition figures ahead of the" vote, he added. But the officials said diplomacy is necessary to cement anti-IS gains and restore regional stability as the administration presses other nations and private companies to help with post-war reconstruction.More news: SC restrains J&K Police from acting on FIR against Army personnel
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