By Dan Williams and Nidal al-Mughrabi

JERUSALEM/GAZA, May 19 (Reuters) - Israeli worries about gunrunner tunnels from the Egyptian Sinai to the Hamas-run Gaza Strip are overblown as the greater smuggling threat is from the Mediterranean sea, a senior Israeli lawmaker said on Monday.

Israel last year accused Egypt of not doing enough to stop arms reaching Palestinian factions, a charge rebuffed by Cairo, though it has since mounted more public crackdowns on tunnels criss-crossing its 12 km (7.5 mile) frontier with coastal Gaza.

A halt to the smuggling is now among Israeli conditions for considering an Egyptian-proposed ceasefire with Hamas in Gaza.

Isaac Ben-Israel, a lawmaker in Israeli Prime Minister Ehud Olmert's party who sits in parliament's key defence committees, said military-grade Hamas rockets recently fired from Gaza into the Jewish state were unlikely to have come in from Sinai.

"To the best of our knowledge, they were smuggled from the sea, not through tunnels," he told Israel's Army Radio.

"In general, we tend to greatly exaggerate the gravity of the subject of arms smuggling from Egypt," Ben-Israel said, adding that he did not agree with assessments that the Gaza-Egypt border is "our main problem" in the territory.

Hamas, an Islamist faction which has been largely isolated in Gaza since routing the forces of Western-backed Palestinian President Mahmoud Abbas there last June, acknowledged bringing in weapons from outside the territory. It gave no details.

Palestinian sources familiar with the flow of munitions said most come in through tunnels from Sinai, which have also done a brisk business in supplying food, fuel and other goods in short supply due to an Israeli-led economic blockade on Gaza.

But Grad and Katyusha-style rockets favoured by Hamas and other factions for hitting targets deep in Israel are too big to be dragged through the underground passages, the sources said.

FLOATED ASHORE

Ben-Israel, an army ex-brigadier and former chief of weapons development at Israel's Defence Ministry, said rockets and other arms have frequently been floated to Gaza's 45 km- (25 mile) long coast in special canisters released by boats out at sea.

In 2002, Israel seized a ship in the Red Sea that it said was delivering 50 tonnes of arms to the Palestinians. According to Israel, the arms were funded by Iran and were to have been loaded onto fishing boats which would have dumped them off Gaza in submersible tubs that Palestinian divers could then recover.

The delivery vessels for such smuggling missions generally come from ports in Egypt or Lebanon, Israeli officials say.

"It is very hard to stop such a thing, because you cannot scour every centimetre of the beach for small containers," Ben-Israel said.

Israeli Defence Minister Ehud Barak was due to fly out to the Red Sea resort of Sharm el-Sheikh later on Monday for talks with Egyptian President Hosni Mubarak on the truce idea.

Barak's office had no immediate response to Ben-Israel's remarks, which echoed rare public comments Mubarak made in December after Israeli Foreign Minister Tzipi Livni angered his government by calling its handling of Gaza's border "terrible".

The weapons used by Hamas and other Palestinian factions in Gaza, Mubarak told Israel's Yedioth Ahronoth newspaper, come "not from Sinai, but mainly by sea."

Yuval Steinitz, a lawmaker from Israel's right-wing opposition who, like Ben-Israel, has access to classified intelligence reports, told Reuters seaborne smuggling accounts for only a "tiny fraction" of arms that reach Gaza. (Editing by Charles Dick)

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