ISMAILIA, Egypt, March 27 (Reuters) - Egypt held a new round of talks with Hamas and Islamic Jihad on Thursday as part of efforts to strike a truce between the Palestinian militant groups and Israel, Egyptian sources close to the talks said.

Egypt, with U.S. blessing, has been trying to negotiate a cessation of hostilities between Israel and the militants from the Hamas-controlled Gaza Strip.

The sources, speaking on customary condition of anonymity, said the talks were held on the Egyptian side of the Rafah border crossing and attended by Hamas official Jamal Abu Hashem and Khaled al-Batsh of Islamic Jihad.

General Mohamed Ibrahim, a senior aide to intelligence chief Omar Suleiman, represented Egypt, they added without elaboration.

Hamas, which took control of the Gaza Strip in June after routing the forces of Palestinian President Mahmoud Abbas, has set out its conditions for a ceasefire with Israel. The conditions include an end of Israeli hostilities and the reopening of the Gaza border crossings.

Hamas has also demanded a say in running the crossings, a condition that Israel rejects. The Jewish state wants Hamas and other militants in the coastal strip to stop cross-border rocket attacks on Israel.

Following earlier talks between Egypt and the Palestinian groups, Cairo released 33 Hamas militants who had been detained after breaching the border wall in Rafah in January. Egypt has also promised to boost power supplies to Gaza. (Reporting by Yusri Mohamed; Writing by Alaa Shahine; Editing by Dominic Evans)

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