Tillerson stressed a need for free and fair elections in all countries ahead of a March presidential vote in Egypt, but withheld direct comment on what critics say is a crackdown on some rivals seeking to challenge President Abdel Fattah al-Sisi at the polls.
It stepped up support for Kurdish-led forces in Syria before its NATO ally Turkey began a military operation against them last month, and has sided firmly with Israel in recognising Al-Quds as its capital, angering Palestinians and drawing rebukes from Arab leaders.
Tillerson and his Egyptian counterpart Sameh Shoukry delivered a message on Monday that relations remained strong with one of the key U.S. Arab allies.
"We agreed we would continue our close cooperation on counterterrorism measures," Tillerson said.
"The U.S. commitment in continuing to support Egypt in its fight against terrorism and bringing security for the Egyptian people is steadfast and will continue," he said.
Shoukry said Cairo and Washington had agreed to hold strategic dialogue talks at the level of foreign ministers later this year.
Tillerson also met Sisi before leaving the country. He was to attend a conference on Iraqi reconstruction in Kuwait.