Suspected militants blew up an empty military office in Sinai on Wednesday as an Al-Qaeda inspired group said it was behind a deadly police headquarters suicide bombing two days earlier.

A security official said suspected militants planted a bomb in a military intelligence office in the town of Rafah bordering the Palestinian Gaza Strip. The office had been vacant since July, the official added.

The blast comes three days after 57 people were killed across Egypt in clashes between Islamists and security forces.

The following day, militants launched a wave of brazen attacks, killing three policemen with a car bomb outside their south Sinai HQ, and attacking a communications satellite dish in Cairo using rocket-propelled grenades.

The Al-Qaeda-inspired group Ansar Beit al-Maqdis claimed responsibility for the police headquarters bomb in a statement posted on militant Islamist Internet forums on Wednesday.

"God has allowed your brothers in Ansar Beit al-Maqdis to target a den of oppression, the police headquarters in south Sinai in the city of El-Tor," the statement said.

The group said a suicide bomber carried out the attack in retaliation for the "killings of thousands of Muslims" when security forces violently dispersed two Islamist protest camps in Cairo on August 14.

That operation killed hundreds of supporters of ousted Islamist president Mohamed Morsi, and more protesters and police died in ensuing clashes.

Dozens of soldiers and policemen have been killed in daily attacks in Sinai, as the army has poured troops and armour into the lawless peninsula to confront a militant insurgency.

Militants there intensified attacks after the army ousted Morsi on July 3.

The country's first democratically elected president, who served just one year in office, is being held at an unknown location.