RAFAH, Egypt, Aug 7 (Yusri Mohamed/Reuters) - Egypt began to seal off smuggling tunnels into the Gaza Strip on Tuesday, a security source said, two days after gunmen shot dead 16 Egyptian border guards in an attack blamed partly on Palestinian militants.

As officials considered how to respond to the deadliest assault along Egypt's tense Sinai Peninsula border with Israel and Gaza in decades, crowds of angry mourners wept at the military funeral of the slain guards in Cairo.

Lawlessness in the rugged desert has spread since the fall of autocrat Hosni Mubarak in an uprising 18 months ago and the election of an Islamist successor whose commitment to security cooperation with Israel has yet to be tested.

A Reuters reporter in the border town of Rafah said heavy equipment was brought to the Egyptian side of the tunnels, which are used to smuggle people to and from Gaza as well as food and fuel that are a lifeline for the small territory's population.

The campaign aims at closing all the openings between Egypt and the Gaza Strip that are used in smuggling operations, said the security source.

The government in Cairo said the gunmen behind Sunday's attack had reached Egypt via the Gaza smuggling tunnels.

Israel says Palestinian jihadi groups have been crossing from Gaza into Egypt and exploiting the security vacuum there by teaming up with local militants with the aim of attacking Israel's long border running south to the Red Sea.

Sinai-based militants sworn to destroying Israel have repeatedly attacked a gas pipeline to the Jewish state as well as Egyptian police stations and security checkpoints. Eight Israelis have been killed in border attacks in the past year.

New Egyptian President Mohamed Mursi quickly pledged to bring the region back under government control after Sunday's attack, the worst since Egypt made peace with Israel in 1979, ending a succession of wars.

No one has claimed responsibility. The Egyptian army said 35 militants were involved and that mortar bombs fired from Gaza landed in the area during the operation.

POLITICAL PROBLEM

Sealing the tunnels will be an uncomfortable move for Mursi who has brought Egypt closer to the Islamist Hamas movement that rules Gaza since he came to power in June, promising to help improve the life of Palestinians there.

Egyptian security forces began arresting suspects in the main northern Sinai town of al-Arish on Tuesday, the security source said, as officials checked the names of potential suspects released from prison since Mubarak was ousted.

Extensive meetings are currently taking place between top officials in the army, interior ministry and border guard to come up with a plan to detect and find the criminals behind Sunday's attacks, a second security source said.

Hamas, also hostile to Israel but seen as too moderate by jihadi groups, has condemned the killings of the Egyptians and has said it is sealing the tunnels from its side while helping Egypt to identify those behind the attack.

In a statement on Tuesday, the office of Ismail Haniyeh, the prime minister of the Hamas government in the Gaza Strip, said he had phoned Mursi to deny involvement in the attack and suggest forming a permanent joint security committee.

PRESSURE TO RESPOND

Egypt's response to the attacks will help define its new relationship with Israel.

Mubarak was a staunch U.S. ally who cooperated closely with Israel to help ensure its security and suppressed Islamists including Mursi's Muslim Brotherhood, which rejected violence to achieve its goals but often voiced hostility to Israel.

Mursi took office in June promising to uphold peace with Israel and the Israelis are looking nervously for proof that he will be as zealous as Mubarak.

Israel sent condolences to Egypt over the attack and sent back the charred bodies of five attackers and an Egyptian soldier who had been forced to drive the vehicle that stormed the crossing into Israel, Egyptian medical sources said.

Mursi announced a state of national mourning, visited the scene of the attack and on Tuesday met some of the seven soldiers injured in the assault in a Cairo military hospital.

Roads were blocked on Tuesday near the main military mosque in Cairo, which was packed with mourners who shouted and jostled to be near the coffins of the dead security guards draped in Egyptian flags. Outside, hundreds prayed in the midday sun.

Thousands, many holding flowers, had gathered by the time the bodies were carried from the mosque for burial.

Some mourners who held Mursi's administration responsible for the deaths rushed at Prime Minister Hisham Kandil and some Islamist politicians as they left the mosque.

You killed them you dogs, they shouted, trying to hit the politicians with their shoes. Mursi did not attend the ceremony.

Any firm proof that the attack was planned and executed from Gaza could be inconvenient for Mursi given the Brotherhood's ties to Hamas. The Brotherhood blamed Israeli intelligence for the attack. Israel dismissed that.

If the attackers came from the Gaza Strip, that would be very embarrassing for the Brotherhood, said a Western diplomat. Rather than allow that to grow in people's minds, they thought they could say this was an Israeli false flag.

The Brotherhood also said it was imperative to review clauses of the 1979 peace deal, which limited the presence of troops in the border zone, echoing recent calls from politicians and commentators for changes to the treaty.

But Mursi's spokesman Yasser Ali said on Tuesday that the president had stressed his commitment to the peace agreement.

Israel indicated that no changes were needed, saying it had agreed in the past to Egyptian requests to deploy more troops.

We proposed aid to them, also to investigate and we also handed over the bodies of the six terrorists. At the moment we are waiting, Israel's Foreign Minister Avigdor Lieberman said on Israeli radio on Tuesday.