CAIRO/ISMAILIA, Egypt (Reuters) - A suicide car bombing killed at least 10 Egyptian soldiers in the Sinai Peninsula on Wednesday, security sources said, one of the deadliest attacks there since militants stepped up violence after the overthrow of Islamist President Mohamed Mursi.
In a separate attack near Cairo, four policemen were wounded by a hand grenade thrown at a checkpoint, a security official said, underscoring the fighters' widening reach.
The Sinai bomb struck a convoy transporting the soldiers near the coastal town of El-Arish, on the road to the border with the Palestinian-controlled Gaza Strip.
Thirty-five people were wounded, security officials said. A military official and state media said it was a suicide attack.
Though there was no immediate claim of responsibility, the attack suggested the al Qaeda-inspired militants still have the means to strike even after the army launched a major security operation this summer in the desert peninsula bordering Israel.
"It is hard to stop them. They have places to hide in the Sinai. From these hiding places they come out, strike and retreat," said a senior security official.
State authority collapsed in North Sinai after President Hosni Mubarak's downfall in 2011, allowing an array of hardline Islamist groups to expand into a security vacuum. A flood of weaponry from Libya following Muammar Gaddafi's overthrow has exacerbated Egypt's security problems, diplomats say.
The army's spokesman pledged to continue the "war on black terrorism" in a posting on his Facebook page.
The security situation and military-imposed restrictions on reporting in North Sinai make it difficult to independently verify reports of attacks.
Israel is deeply concerned about the danger posed by Sinai-based militants, who have also targeted merchant shipping passing through the Suez Canal, a vital world shipping artery controlled by Egypt.
"More such terrorist operations can be expected," said Mohamed Gomaa, a political analyst at the Al-Ahram Center for Political and Strategic Studies in Cairo, adding the army would need to send reinforcements.
Mursi was ousted on July 3 after mass protests against his rule. The downfall of Egypt's first democratically elected head of state has also triggered attacks beyond Sinai in the towns and cities of the densely populated Nile Valley, raising concern the country may face a sustained campaign of violence.
That, together with political tension between Mursi's Muslim Brotherhood and the army-backed government, is weighing on investment and tourism in Egypt, an important U.S. ally.
This week, gunmen shot dead a senior security officer outside his home in Cairo. A Sinai-based militant group, Ansar Bayt al-Maqdis, claimed responsibility for the killing, according to a statement posted on a militant Islamist website.
The same group has also said it was behind a failed suicide attack on Egypt's interior minister in September. Police arrested a suspect in that attack in the Nile Delta province of Sharqiya on Wednesday, a security official said.
More than 150 members of the security forces have been killed in Sinai since Mursi was deposed by the army.
Militants killed 24 policemen in an ambush in North Sinai in August, days after security forces killed hundreds of Mursi supporters while dispersing their sit-in protests in Cairo.
Wednesday's attack was the bloodiest against the military in Sinai since August last year, when 16 soldiers were killed by militants who stole two army vehicles which they then used in a cross-border raid into Israel.
The Muslim Brotherhood has condemned violence and says it is committed to peaceful activism. But many of its leaders are standing trial for inciting violence.
In Sinai, the army has used attack helicopters, tanks and other heavy weapons in its campaign.
"They're fighting an insurgency using very forceful means," said Anna Boyd, manager for country risk in the Middle East and Africa at IHS Jane's based in London. She said this risked further radicalising the population.
Writing by Michael Georgy/Tom Perry; Editing by Andrew Heavens