(Adds quotes from prime minister)
By Michael Georgy
CAIRO, Sept 2 (Reuters) - An attack on a convoy killed 11 members of the Egyptian security forces in the Sinai Peninsula on Tuesday, security and medical sources said.
Two were killed by a roadside bomb and the others were shot as they tried to flee, the security sources said. Security sources said earlier that the attack killed 10 soldiers.
Militants in Sinai have stepped up attacks on policemen and soldiers since then-army chief Abdel Fattah al-Sisi toppled President Mohamed Mursi of the Muslim Brotherhood in July 2013.
Sisi was elected president three months ago and his government makes no distinction between the Brotherhood -- which says it is a peaceful movement -- and the Sinai militants.
The attacks initially targeted security forces in Sinai -- a remote but strategic part of Egypt located between Israel, the Gaza Strip and the Suez Canal -- but they have since extended their reach, with bombings on the mainland.
The violence has hurt tourism, a pillar of the economy.
Prime Minister Ibrahim Mehleb condemned Tuesday's attack and said Egypt would continue to confront terrorism. "The world has witnessed now what the hands of terrorism are doing in our country," he said in a statement. "Terrorism will not succeed in breaking the will of Egyptians."
The Sinai-based militant group Ansar Bayt al-Maqdis said in August it had beheaded four Egyptians, accusing them of providing Israel with intelligence for an air strike that killed three of its fighters.
Egyptian security forces have launched several offensives in Sinai in a bid to eliminate Ansar, widely regarded as the country's most dangerous militant group.
Chaos in Libya, meanwhile, has allowed militants to set up makeshift training camps only a few kilometres from Egypt's border, according to Egyptian security officials.
The militants, those officials say, harbour ambitions similar to the al Qaeda breakaway group, Islamic State, that has seized large swathes of Iraq; they want to topple Sisi and create a caliphate in Egypt.
In July, gunmen killed 21 Egyptian military border guards near the frontier with Libya, highlighting a growing threat from an area that security officials say has become a militant haven.
The Sinai insurgency has shown how even a small number of militants can mount a challenge to the Egyptian state. Ansar has killed hundreds of people and proved resilient in the face of army offensives, yet Sinai residents say its core amounts to only a few hundred militants.
Any alliance between Ansar and the militants near the Libyan border could pose big problems for Egypt, which is aching for stability after three years of unrest since the start of the Arab uprisings. Members of Ansar say contacts between the two groups have already been established.
Islamists and the Egyptian state are old enemies. Islamist-leaning army officers assassinated President Anwar al-Sadat in 1981, mainly because of his peace treaty with Israel; and former President Hosni Mubarak fought insurgents in the 1990s.
But the lightning seizure of large swathes of Iraq by Islamic State has added to the sense of urgency in combating militants along Egypt's border with Libya and in the Sinai. (Editing by Dominic Evans)