US Secretary of State Hillary Clinton is to meet the head of Egypt's top military council, Field Marshal Mohamad Hussein Tantawi, on the second day of her visit to the country.
She has said she will urge the armed forces, which assumed power after last year's revolution, to return "to a purely national security role".
On Saturday, Mrs Clinton met new President Mohammed Mursi.
Mr Mursi and the military have been in conflict over parliament's dissolution.
The Supreme Council of the Armed Forces (Scaf) shut down the chamber, dominated by Mr Mursi's Islamist allies, before he was formally sworn in last month.
It also stripped the new president, elected in the country's first freely contested leadership vote earlier in June, of many of his powers.
Mr Mursi, of the Muslim Brotherhood's Freedom and Justice Party, tried to reinstate parliament by decree last weekend. The Supreme Constitutional Court has said the dissolution is final.
As head of the Scaf, Field Marshal Tantawi became Egypt's interim ruler after the fall of President Hosni Mubarak in February last year.
'Cordial'After meeting Field Marshal Tantawi and other army leaders on Sunday, Mrs Clinton will head to Egypt's second city, Alexandria, a stronghold of the Muslim Brotherhood. Continue reading the main storyAnalysis
Kim Ghattas BBC News, Cairo
Hillary Clinton wanted to come to Egypt soon after the elections because the US believes it is important to engage with President Mursi early on. The meeting was described by officials as good and candid but this is still a tentative relationship, not a full embrace.
The US administration is slowly feeling its way in the region, learning to work with groups that Washington has shunned in the past.
When Condoleezza Rice was here in 2005 as US secretary of state, she was categorical - the US would not engage with the Muslim Brotherhood. But in the new Arab world, long-held American assumptions about who is a friend or not have been shattered. And new problems have emerged.
Outside Mrs Clinton's hotel, dozens of Egyptians protested against Mr Mursi and continued US military aid to Egypt under his presidency with slogans like: "We don't want Hamas to rule Egypt."
There she will meet leading women, the Coptic Christian community and young entrepreneurs. She is then due to fly on to Israel.
During her meeting with Mr Mursi on Saturday, Mrs Clinton said the situation required "compromise and real politics".
"Democracy is hard," she said.
She praised Egypt's military council for its interim leadership, "for representing the Egyptian people in the revolution as compared to what we are seeing in Syria which is the military murdering their own people".
But she also voiced support for a "full transition to civilian rule".
The secretary of state also encouraged President Mursi to live up to promises to protect the rights of women and minorities, and to preserve the peace treaty with Israel.
The hour-long meeting between President Mursi and Mrs Clinton was described by a US official as candid and cordial.
However, on Saturday evening hundreds of demonstrators gathered outside Mrs Clinton's Cairo hotel, chanting anti-Islamist and anti-US slogans in protest at her visit. Some brandished posters depicting the field marshal.
Another protest outside the US embassy was organised by Coptic Christian youth activists, who chanted: "They both can't be trusted, not the Americans, not the Brotherhood."
The BBC's Jon Leyne in Cairo says that for all the US fears of an Islamist takeover in recent decades, the governments in Washington and Egypt have now realised they need each other.
Mr Mursi and the Muslim Brotherhood are particularly keen to avoid the sort of international isolation so damaging to other Islamist governments after they have taken office, our correspondent says.