CAIRO, July 15 (Reuters) - At least three people were killed and 17 wounded when suspected militants fired rocket-propelled grenades at a bus carrying workers in Egypt's North Sinai province early on Monday, security and medical sources said.

Witnesses said the attackers shouted "Allahu akbar!" (God is greatest) after hitting the vehicle in the city of El Arish, at the centre of a sharp rise in Islamist militant attacks since Egypt's President Mohamed Mursi was ousted by the military on July 3.

Egypt's army said a "terrorist group" had meant to hit a police vehicle but missed and hit the bus instead. The military statement on its spokesman's Facebook page said the attack took place on the road to El Arish.

Hardline Islamist groups based in North Sinai, a lawless region bordering Israel and the Gaza Strip, have intensified attacks on police and soldiers over the past two years, exploiting a security vacuum following the 2011 uprising that ousted autocratic President Hosni Mubarak.

The violence has spiked again since Mursi's overthrow, and militants have attacked security checkpoints and other targets on an almost daily basis, killing at least 13 people and wounding dozens.

Mursi's Muslim Brotherhood suggested the increase in violence could have been be engineered by the army itself.

"We do not rule out that the violence on the ground in beloved Sinai are contrived events," said Brotherhood spokesman Ahmed Aref in a statement posted online.

"Incidents of violence against civilians and the police and the army in Sinai are the work of the intelligence service intended to distort ... revolutionary peaceful protests by our people in Sinai against the military coup," senior Brotherhood leader Essam El-Erian said in a statement posted on his Facebook page.

No one was immediately available from the army to respond to the accusation.

The workers on the bus attacked on Monday were employed at a cement factory, said security sources. (Reporting by Yusri Mohamed in Ismailia and Yasmine Saleh, Shadia Nasralla and Ali Abdelaty in Cairo; Writing by Mike Collett-White; Editing by Christopher Wilson and Andrew Heavens)