ISMAILIA, Egypt, Sept 28 (Reuters) - An Egyptian soldier was shot dead in the Sinai Peninsula on Saturday, security officials said, and militants released a video showing attacks against the army in the region where the state is trying to stamp out al Qaeda-linked fighters.

The soldier, a conscript, was shot while standing guard by a government building the town of Sheikh Zuweid, close to the border with the Gaza Strip, the sources said. He was hit in the stomach.

Militant Islamists have stepped up attacks on security forces in Sinai since the army deposed President Mohamed Mursi of the Muslim Brotherhood on July 3. The army spokesman said on Sept. 15 that more than 100 members of the security forces had been killed in Sinai since Mursi's downfall.

The militants expanded into a security vacuum left by the 2011 downfall of veteran autocrat Hosni Mubarak. Since Mursi was ousted, they have mounted almost daily attacks.

One of the groups, Ansar Bayt al-Maqdis, posted a video on a jihadist website showing what appeared to be a roadside bomb attack on one armoured vehicle in Sinai. In a second attack caught on camera, a parked armoured vehicle was engulfed by an explosion after a man is seen placing something beneath it.

It did not specify where or when the attacks took place.

The video also included images of the aftermath of a third attack, showing what appeared to be human remains near an army vehicle that had been hit.

Ansar Bayt al-Maqdis, meaning "Supporters of Jerusalem", claimed responsibility for a Sept. 5 suicide bomb attack in Cairo that tried to assassinate the interior minister. He survived unscathed.

The group first appeared in 2012, when it claimed responsibility for bomb attacks on a pipeline being used to export gas to Israel. Its stated aim was to mount a holy war against Israel from Egyptian territory.

But since Mursi's downfall it has turned its attention to attacking Egyptian security forces in Sinai and has issued statements demanding they leave the territory.

(Reporting by Omar Fahmy and Yousri Mohamed; Writing by Tom Perry; editing by David Evans)