Kerry became the highest-ranking US official to meet President Abdel Fattah al-Sisi since he came to power earlier this month, as part of a rocky transition to democracy since the ousting of long-time leader Hosni Mubarak in 2011.
The top US diplomat's tour is also focused on trying to find a political solution in Iraq, where Islamic militants were today making new gains in an offensive that has triggered international alarm.
"We also discussed the essential role of a vibrant civil society, free press, rule of law and due process in a democracy."
Kerry's call for a free press in Egypt comes as a court tomorrow is due to deliver its ruling in the trial of three Al-Jazeera journalists and 17 other co-defendants, accused of aiding the blacklisted Muslim Brotherhood of ousted president Mohamed Morsi.
"Obviously this is a critical moment of transition in Egypt, enormous challenges," Kerry said in Cairo as he met new Foreign Minister Sameh Shoukri.
But he vowed that "the US is very interested in working closely" with the new government "in order to make this transition as rapidly and smoothly as possible".
Since Egypt's first freely elected leader Morsi was toppled by Sisi in July 2013, a government crackdown on his supporters has left more than 1,400 people dead in street clashes and at least 15,000 jailed.
US officials also revealed that USD 572 million in aid, which had been frozen since October, was released to Egypt about 10 days ago after a green light from Congress. It will mainly go to pay existing defence contracts.
"The Apaches will come and they will come very, very soon," Kerry said minutes before he ended his trip.
Before flying to Amman, Kerry called on "Iraq's leaders to rise above sectarian considerations... And speak to all people," and insisted that Washington is not responsible for the current crisis roiling that country.
