JERUSALEM, Dec 19 (Reuters) - Two Israeli government ministers said on Wednesday they did not rule out third-party mediation with Hamas Islamists who control the Gaza Strip to try to bring an end to rocket fire into southern Israel.

Israel refuses to negotiate directly with Hamas, which seized control of the Gaza Strip in June after routing forces loyal to Palestinian President Mahmoud Abbas. But Israel has used Egyptian and other mediators in the past.

Tensions between Israel and Gaza militants have escalated in recent days. Israel has killed 13 militants in its most deadly air strikes in months against fighters behind rocket attacks from the Hamas-run territory.

The ministers' comments came after Israel's Channel 2 television reported on Tuesday that Hamas's leader in Gaza, Ismail Haniyeh, was prepared to hold negotiations to end militant rocket fire and Israeli attacks.

Haniyeh's aide later denied the report, but reiterated a Hamas proposal for a reciprocal ceasefire in Gaza and the West Bank. Israeli officials said they knew of no new Hamas overtures for talks.

"I think mediation is something to think about," Israeli Transporation Minister Shaul Mofaz told Army Radio.

But Mofaz made clear that Israel was not changing its demands that Hamas stop violence and recognize Israel, benchmarks set by major Western powers.

Israeli cabinet minister Ami Ayalon also said Israel should not rule out speaking to "anyone" in order to stop rocket attacks from Gaza, but urged caution to ensure a ceasefire would not lead to a strengthening of Hamas.

Israeli Prime Minister Ehud Olmert's office played down prospects for even indirect talks with Hamas over rockets.

"Israel will negotiate with Palestinian leadership that accepts the benchmarks of the international community," said Olmert's spokesman Mark Regev. "Until Hamas accepts those benchmarks, it cannot be a partner for dialogue. Our partner is the (Abbas) government."

(Writing by Ari Rabinovitch; Editing by Samia Nakhoul)

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