(Adds deaths of three militants)
CAIRO, April 13 (Reuters) - Egypt has arrested a veteran of the Syrian civil war on suspicion of planning terrorist acts inside Egypt, the state news agency reported on Sunday.
The Egyptian prosecutor's office in Suez City ordered the arrest of Wael Ahmed Abdel Fattah for 15 days, MENA reported, adding that he was suspected of working with Islamist militant groups.
MENA said Abdel Fattah, a former oil company employee, battled in Syria alongside the Nusra Front, seen as the most effective rebel group fighting Syrian President Bashar al-Assad.
Since the army toppled President Mohamed Mursi of the Muslim Brotherhood last July, Islamist militants based in the Sinai Peninsula have stepped up attacks on police and soldiers, killing hundreds. The insurgency has spread to Cairo and other cities, where senior security officials have been targeted.
Militant violence and political turmoil have dealt a heavy blow to tourism, which was a critical source of hard currency during more stable times.
The Egyptian state and militants are old foes. Islamist-leaning soldiers assassinated President Anwar al-Sadat in 1981, mainly because he signed a peace treaty with Israel.
It took former president Hosni Mubarak years to put down an Islamist insurgency in the 1990s.
Egypt's army-backed government says it will defeat Islamist militants, who carry out shootings and bombings.
It's not clear how many Egyptian militants have fought in Syria but any serious numbers returning from the battlefield could complicate efforts to contain violence if they wage a holy war at home.
Egyptian militants who fought in Afghanistan against Soviet occupation troops in the 1980s returned home and eventually trained their weapons on Mubarak's pro-Western government.
Islamist militants currently active in Egypt carry out nearly daily attacks. Egyptian soldiers killed three militants on Sunday as they tried to attack a checkpoint in the north Sinai town of Sheikh Zuwaid, the military said.
Four other militants who were observing the movements of soldiers were arrested.
Army offensives have failed to break militant networks in the Sinai, which is near the border with Israel.
(Reporting by Michael Georgy; Editing by Tom Heneghan)