Kerry made clear that in all his meetings, he conveyed the message that Egyptians who rose up and overthrew Mubarak "did not risk their lives to see that opportunity for a brighter future squandered."
On Saturday, he told the country's bickering politicians that they must overcome differences to get Egypt's faltering economy back on track and maintain its leadership role in the volatile Middle East.
The U.S. is deeply concerned that continued instability in Egypt will have broader consequences in a region already rocked by unrest.
U.S. officials said Kerry planned to stress the importance of upholding Egypt's peace agreement with Israel, cracking down on weapons smuggling to extremists in the Gaza Strip and policing the increasingly lawless Sinai Peninsula while continuing to play a positive role in Syria's civil war.
The impact of Kerry's message of unity to the opposition coalition seemingly was blunted when only six of the 11 guests invited by the U.S. Embassy turned up for a Saturday session with him and three of those six said they still intended to boycott the April parliamentary election, according to participants.
Kerry said that the U.S. would not pick sides in Egypt, and he appealed to all sides to come together around human rights, freedom and speech and religious tolerance.
In an apparent nod to the current stalemate in Washington over the U.S. federal budget, Kerry acknowledged after meeting Foreign Minister Kamel Amr that compromise is difficult yet imperative.
"I say with both humility and with a great deal of respect that getting there requires a genuine give-and-take among Egypt's political leaders and civil society groups just as we are continuing to struggle with that in our own country," he said. "There must be a willingness on all sides to make meaningful compromises on the issues that matter most to all of the Egyptian people."
The opposition accuses Morsi and the Brotherhood of following in the footsteps of Mubarak, failing to carry out reforms and trying to install a more religiously conservative system.
Morsi's administration and the Brotherhood say their foes, who have trailed significantly behind Islamists in all elections since the uprising against Mubarak, are running away from the challenge of the ballot box and are trying to overturn democratic gains.
After meeting Morsi and his defense and intelligence chiefs on Sunday, Kerry flew to Riyadh, Saudi Arabia, and planned later stops in the United Arab Emirates and Qatar, where his focus is expected to be the crisis in Syria and Iran.
Kerry is set to return to Washington on Wednesday.
Associated Press writer Aya Batrawy contributed to this report.