Israel's cross-border strikes in Syria on Saturday - which the Israelis said were in response to an Iranian drone's penetration of its airspace from that territory - give even greater urgency to one of Tillerson's top priorities for the trip: managing the aftermath of the expected final defeat of the Islamic State in Syria.
US officials allowed on Friday that most of Tillerson's discussions would be hard, singling out those in North Atlantic Treaty Organisation ally Turkey as especially prickly given Turkish military action against USA -backed Kurdish rebels in northern Syria and escalating anti-American rhetoric in Ankara.
Tillerson who addressed a press conference after holding a meeting with the Egyptian foreign affairs minister Sameh Shoukry, emphathised with Egypt which has suffered several terror attacks from the Islamic State (ISIS) and other terrorist organisations.
Tillerson will raise human rights issues with Sisi, according to the USA officials, who previewed the trip on condition they not be identified.
The Egyptian military campaign comes ahead of presidential election in March, in which President Abdel Fattah al-Sisi is seeking a second term in office. The opposition is calling for a boycott of the vote, after serious challengers were either arrested or forced to quit the race.
Building on Vice President Mike Pence's recent visit to Cairo, Secretary of State Rex Tillerson plans to strengthen a shared commitment between the United States and Egypt to fight terrorism.
In Kuwait on Tuesday, Tillerson will attend a conference focusing on how to reconstruct a devastated Iraq in the years and decades ahead, relying largely on private-sector companies and global financial organisations.
Mike Pence Has No Interaction With North Korean Officials as Olympics Begin
North Korean delegation lands at Incheon airport before the opening ceremony of the Pyeongchang Winter Games . North and South Korea made a joint entrance under a unified Korean Peninsula flag at the opening ceremony .
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.
They also discussed the Israeli-Palestinian peace process and Mr Tillerson said the United States administration "remains committed to achieving a peace agreement between Israelis and the Palestinians".
"We highly value the support the USA gives us in this war", Shoukry said.
Tillerson's visit to Egypt is the second this year by a top-level US official. Some 2,300 representatives from the private sector, including from more than 100 American companies, are slated to attend.
In Kuwait City, Tillerson will meet Kuwaiti officials who are attempting to mediate a resolution to disagreements between Qatar against its Arab neighbors Bahrain, Saudi Arabia and the United Arab Emirates.
The decision to recognise Jerusalem as Israel's capital led to clashes in the West Bank, and was opposed by Arab and European Union countries. Jordan, which has a large Palestinian population, including refugees, is among the most concerned. The U.S. officials said Tillerson will repeat warnings for Turkey to show restraint in military operations in Kurdish areas of Syria.
Trump administration policies will be the centre of Tillerson's talks in Amman.