(Adds Hamas source, details, background)

By Alaa Shahine

CAIRO, Jan 14 (Reuters) - The Palestinian movement Hamas has presented Egyptian mediators a "detailed vision" on how to carry out a truce initiative proposed by Cairo, which will now relay this vision to Israel, Hamas officials said on Wednesday.

The Islamist group, which rules the Gaza Strip, said it has no objections to the broad ideas of the Egyptian initiative to bring an end to Israel's 19-day offensive on the coastal enclave, which has killed more than 1,000 Palestinians.

But a Hamas source said the group gave Egypt its views on how to carry out essential parts of the ceasefire plan, including the operation of the Rafah crossing and was seeking assurances that Israel would lift its blockade on the strip.

"The movement has presented a detailed vision to the Egyptian leadership so that it (Egypt) can continue its pursuit to end the aggression and lift the injustice on our people in the Gaza Strip," Hamas official Salah al-Bardawil said.

"The Egyptian leadership will ... discuss (the views) with the aggressor to reach the goals that we want. During this period we will monitor," he told a news conference after talks with Egyptian intelligence officials in Cairo.

Israeli officials were expected in Cairo on Thursday to hold talks with Egyptian intelligence officials.

Osama Hamdan, Hamas' representative in Lebanon, said earlier on Wednesday that points of difference remained over the Egyptian plan.

The Egyptian proposal calls for a temporary ceasefire, followed by a long-term truce and the opening of Gaza's border crossings in the presence of officials from the Palestinian Authority led by President Mahmoud Abbas, whose forces Hamas drove out of Gaza in 2007.

Hamas official Mohammed Nazzal told Al Arabiya television that Islamist group had no problems with the presence of European or Turkish monitors on the borders of the Gaza Strip "along with the Palestinian Authority's security forces and those of the government in Gaza."

"If there are fears about the entry of arms through the Rafah crossing, those European observers would be present ... and everything could be inspected," he said.

But the Hamas source said the group fears Israel would control the movement of any monitors as it did under a 2005 deal to open the Rafah border crossing, which links Gazs with Egypt.

"Everybody in Gaza remembers how it was under the 2005 agreement. The Zionist enemy could anytime prevent the European monitors from going and say the crossing is closed," the source told Reuters on condition of anonymity.

He said Hamas wanted guarantees that Israel would lift the blockade on the strip "otherwise we will go back to what used to happen during the first six-month truce," he added, referring to an Egyptian-brokered deal which expired in December.

The Jewish state has said it had to close the Gaza crossing frequently because of security concerns.

Israel wants an end to Hamas rocket attacks on its towns and assurances the movement will be unable to rearm itself by smuggling from Egypt.

Ten Israeli soldiers and three civilians hit by rockets fired from the Gaza Strip have been killed since Israel launched its campaign on Dec. 27.

The Hamas source said if Egypt came back with a positive response from Israel on Hamas' demands "We will be ready to start (the ceasefire) immediately". (Editing by Matthew Jones)

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