BERLIN, May 30 (Reuters) - The quartet of Middle East mediators said on Wednesday it planned to meet the Israelis and Palestinians next month as well as the Arab League in a bid to revive peace hopes further dimmed by a new round of violence.

After a meeting in Berlin, the quartet expressed strong concern over new fighting involving both Hamas and Fatah forces in Gaza as well as Israel, which says it is defending itself from rockets fired by Hamas into the Jewish state.

It called on all sides to respect a ceasefire, for Israel to use restraint and urged Palestinian President Mahmoud Abbas to do "everything to restore law and order", including the release of kidnapped BBC journalist Alan Johnston.

The quartet also condemned the firing of rockets into southern Israel and the build-up of arms by Hamas and other militant groups in Gaza.

Israel killed two Hamas militants in an air strike in the Gaza Strip on Wednesday and said it was not considering a ceasefire with the Islamist group despite appeals from Abbas, whose Fatah party formed a unity government with Hamas two months ago.

Hamas says any ceasefire must include an immediate end to all Israeli attacks in both territories, a demand rejected repeatedly by Israel.

Comprising the United States, Russia, the United Nations and the European Union, the quartet announced plans for talks with the Israelis and the Palestinians at an undisclosed time and location in June as well as with the Arab League.

"Looking ahead, the quartet discussed a calendar for the coming months to support and encourage progress on the bilateral and regional tracks," said a quartet statement.

It also urged Israel to transfer about $700 million in tax and customs revenues into a European-run mechanism used to get funds to the Palestinians while avoiding Hamas, which is under a quartet embargo for direct aid.

Such a transfer would improve the economic and humanitarian conditions in the West Bank and Gaza, the quartet said.

In Gaza, Hamas official Sami Abu Zuhri said the quartet's statement had "only served Israel" and made it party to the conflict.

"These demands are rejected and they only strengthened our belief that the Quartet committee did nothing but serve the interests of the Israeli occupation," said the Hamas official. (Additional reporting by Nidal al-Mughrabi in Gaza)

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