ISMAILIA, Egypt, May 25 (Reuters) - Three soldiers were killed in a bombing of an armoured vehicle by Islamist militants in Egypt's Sinai Peninsula, security and medical sources said on Thursday.

The soldiers were conducting a patrol in the North Sinai town of Rafah which borders the Gaza Strip.

In a separate attack, a policeman was killed by gunmen while he was shopping in Arish, the capital of North Sinai province. The gunmen were able to flee and the body was taken to a military hospital.

The attacks are the latest in an area where security forces have been battling Islamic State, which authorities say has killed hundreds of members of the security forces.

The militants have also extended their campaign to other parts of Egypt, most recently attacking churches in Cairo and other cities with the loss of dozens of lives.

No immediate official comment was available from the military or the interior ministry. No group has yet claimed responsibility for the attack.

(Reporting by Yousri Ahmed,; Writing by Ahmed Aboulenein, editing by Ed Osmond) ((ahmed.aboulenein@thomsonreuters.com; +20 2 2394 8097; Reut