The Electoral Commission in Egypt has confirmed the two candidates who will contest a presidential run-off in June are Ahmed Shafiq and Mohamed Mursi.
Mr Shafiq is the last prime minister under Hosni Mubarak and Mr Mursi is the Muslim Brotherhood candidate
Two of the defeated candidates earlier demanded a recount, citing violations. But the commission dismissed the claims by Hamdin Sabbahi and Abdul Moneim Aboul Fotouh.
Last week's voting was Egypt's first freely contested presidential election.
Electoral Commission head Farouq Sultan said Mr Mursi won 5.8 million votes and Mr Shafiq secured 5.5 million.
"No candidate won an outright majority, so according to Article 40 of the presidential election law, there will be a run-off between Mursi and Shafiq,'' he said.
The commission said turnout in the first round on 23-24 May was 46%. About 50 million people were eligible to vote.
The final round will be held on 16-17 June.
The Supreme Council of the Armed Forces has promised a fair vote and civilian rule.
