David Cameron has met Egypt's new leaders, as the first world leader to visit the country since President Hosni Mubarak was forced out of office.
The UK prime minister held talks with the head of the armed forces supreme council Mohamed Tantawi and caretaker Prime Minister Ahmed Shafiq.
He said Egypt had a "great opportunity" to push for democracy.
Mr Cameron also described the violent suppression of protests in neighbouring Libya as "appalling".
Egypt's long-standing leader Mr Mubarak stood down 10 days ago amid widespread protests against his regime by pro-democracy activists.
Speaking on the flight to Cairo, Mr Cameron said: "This is a great opportunity for us to go and talk to those currently running Egypt to make sure this really is a genuine transition from military rule to civilian rule, and see what friendly countries like Britain and others in Europe can do to help."
Part of the prime minister's agenda will be a call for the lifting of emergency laws, which have been in place for more than 30 years.
Mr Cameron walked through Tahrir Square, the centre of the anti-Mubarak demonstrations, and met figures from the protest movement, although not representatives of the Muslim Brotherhood - the banned Islamic group which is thought to have widespread public support.
The prime minister had planned to make a trade-centred tour of the Middle East but altered his schedule to visit Egypt.
He told the BBC that Egypt's current military rulers had done some good things in terms of setting out the need for constitutional change, a referendum and parliamentary elections.
But he said they need to "do more, more quickly in terms of ending the state of emergency, allowing political parties to register and freeing political prisoners".
Mr Cameron said he had met "very brave" figures from the protest movement who "don't yet have confidence that this transition is real".
"As a friend of Egypt we want this transition to happen we want to help encourage the government to take those steps," he said.
BBC deputy political editor James Landale, who is travelling with Mr Cameron, said it was extraordinary for a British prime minister to engage in full-on diplomacy in a country that was still "in flux".
He said the prime minister believed that there was a window of opportunity for western leaders to give what his advisers are calling "candid" advice, but there was a danger he could be seen as lecturing or as legitimising a temporary regime.
But Mr Cameron said it was "right to come here to say that we support the aspirations of people in Egypt for a more genuine, open democracy".
"It's not a question of either lecturing or legitimising, it's saying we want Egypt to have a strong and successful future," he said.
The Egypt visit comes while anti-government protests are raging in Libya and Bahrain.
Asked about the violent treatment of demonstrators against Muammar Gaddafi's regime in Libya in recent days, Mr Cameron said: "We can see what is happening in Libya which is completely appalling and unacceptable as the regime is using the most vicious forms of repression against people who want to see that country, which is one of the most closed and one of the most autocratic, make progress."
UK Foreign Secretary William Hague has been in Brussels for talks on the violence in Libya.
Oil firm BP has said it is preparing to evacuate some of its staff and their families from the country over the next day or so. The company has 40 foreign employees in Libya.