* Two bombs in South Sinai kill soldier, wound at least eight
* Two bombs in Cairo kill two people
* Presidential elections to be held later this month (Adds car bomb in central Cairo, details)
By Shadia Nasralla and Tom Perry
CAIRO, May 2 (Reuters) - Two suicide bombings in Egypt's South Sinai killed a soldier and wounded at least eight people and two other bombs killed two people in Cairo on Friday, less than four weeks before a presidential election is due to be held, official sources said.
In other violence in the port city of Alexandria, two people were shot dead when supporters of deposed President Mohamed Mursi clashed with residents, the Interior Ministry said in a statement.
Militant attacks and other political violence have spiralled since the army overthrew Mursi, a senior Muslim Brotherhood figure, last July after mass protests against his rule.
Former army chief Abdel Fattah al-Sisi, who led the action, is expected to win the presidential election on May 26 and 27.
Friday's suicide attack in El-Tur, a town on the main road between Cairo and the tourist resort of Sharm El-Sheikh, killed a soldier as well as the bomber. Three policemen and another soldier were wounded, an Interior Ministry statement said.
Four Egyptians were wounded in the second attack, further south on the road between El-Tur and Sharm El-Sheikh, the Interior Ministry and security sources said.
A spokesman for the governorate of South Sinai province, speaking to CBC television, identified the wounded as employees of a tourism company. The Interior Ministry said they were factory workers.
A third bomb killed one policeman at a traffic security post near a courthouse in Cairo, security sources said. At least four other policemen were wounded, the Interior Ministry said.
In a fourth blast, one person was killed when a car exploded near a metro station in downtown Cairo, security sources said.
The army has been waging a campaign against armed Islamist groups in North Sinai. The influence of such groups expanded in the area after the 2011 uprising that toppled Hosni Mubarak from the presidency.
While most of the recent attacks have targeted the security forces, three South Koreans were killed in February when a bomb hit a tourist bus in South Sinai near a border crossing with Israel.
Tourists are an important source of foreign currency for Egypt's economy but tourist numbers have dwindled over more than three years of political turmoil.
In the Alexandra clashes, two people were shot, the Interior Ministry said. Forty-two Mursi supporters were arrested in protests across Egypt, it added.
Three members of the security forces were wounded in clashes with Brotherhood supporters in Helwan, south of Cairo, it said.
The Brotherhood, on its website, blamed one of the deaths in Alexandria on security forces. Thousands of Brotherhood supporters have been arrested and hundreds killed since July. The organisation says it is committed to peaceful activism.
Underlining political tensions, an Egyptian court sentenced the leader of the outlawed Muslim Brotherhood and 682 supporters to death earlier this week, intensifying a crackdown on the movement and drawing Western criticism.
The European Union has described the verdict as a breach of international human rights law.
(Editing by Angus MacSwan)
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