EU foreign policy chief Catherine Ashton says Egypt's ousted President Mohammed Morsi is "well", but that she does not know where he is being held.
Baroness Ashton said she had two hours of "frank, in-depth" discussions with Mr Morsi on Monday, without giving further details of the conversation.
Mr Morsi had access to news and followed developments, she added.
She is the first foreign diplomat to meet Mr Morsi since he was detained after being overthrown on 3 July.
Lady Ashton's second visit to Egypt in 12 days comes after more than 70 Morsi supporters were killed in clashes with security forces on Saturday.
She held talks with the interim leadership, including army chief Gen Abdul Fattah al-Sisi and representatives of Mr Morsi's Muslim Brotherhood.
The ousted leader's allies said they were planning a major protest in Cairo on Tuesday, and the interim government has warned that any violation of the law will be dealt with "firmly".
Security officials also threatened to dismantle the main protest sit-in at a square near the Rabaa al-Adawiya mosque in the capital's north-east, where Saturday's deadly clashes erupted.
'Pleased to see me'
Lady Ashton told the BBC that after a night journey involving a helicopter ride and other forms of transport, she met Mr Morsi at a military facility.
She said the deposed president was in "good health" and "good humour".
"He had been told about half an hour before I arrived that I was coming. He was, I think, pleased to see me," she said.
"He is there with two advisers. They are there together. It is a military place. The people around him do care for him. I looked at the facilities."
She described the talks as "friendly, open and very frank" but refused to elaborate further on their content.
"I'm not going to put words into his mouth," Lady Ashton said.
She added that the ousted leader had "access to information, in terms of TV and newspapers, so we were able to talk about the situation, and we were able to talk about the need to move forward".
She said there was a strong desire among leaders from all sides to find a way out of the crisis.
EU officials will keep up discussions to pursue elements that came up during Lady Ashton's visit, and she said she was ready to come back at any time if that would help.
Also on Tuesday US Senators Lindsey Graham and John McCain announced they would travel to Egypt next week at the request of President Barack Obama, to urge military commanders there to start moving towards elections.
"We can go over and reinforce in a bipartisan fashion the message that we have to move to civilian control," said Mr Graham. "The military is going to have to, you know, allow the country to have new elections and move toward an inclusive, democratic approach."
The Republican senators would send the message that "jailing the opposition is more and more like a coup", Mr Graham added.
The US sends $1.5bn (£985m) in aid to Egypt every year, most of it to the Egyptian military. But the US would be forced to suspend its programmes if it recognises Mr Morsi's removal as a coup.
The BBC's Jim Muir in Cairo says Mr Morsi's allies insist he must be restored to the presidency, and say they will continue their vigorous and very big street protests until that happens.
But the interim presidency has insisted there will be no deviation from the transition plan, which does not involve Mr Morsi's reinstatement or involvement in the political process.
Mr Morsi has been formally remanded in custody at an undisclosed location, according to a judicial order.
He has been accused of the "premeditated murder of some prisoners, officers and soldiers" when he and several Muslim Brotherhood leaders were freed during a breakout at a Cairo prison in January 2011.
He is alleged to have plotted attacks on jails in the uprising that overthrew President Hosni Mubarak.
Mr Morsi is also accused of conspiring with the Palestinian militant group Hamas, which governs the Gaza Strip and has strong links with the Muslim Brotherhood.
But Hamas has denied any interference in internal Egyptian politics.
On Tuesday, a senior Hamas official told journalists he had proof that the rival Fatah movement fabricated reports to implicate Hamas in clandestine activities in Egypt.
Salah Bardawil showed letters he said were exchanged between Fatah officials and the Palestinian embassy in Cairo.
One letter reportedly suggested that grenades carrying the Hamas logo be used to implicate the movement in violence in Cairo; another is said to have proposed circulating false reports about car bombs being prepared by Hamas for use in Egypt.