As officials weighed how to strike back after the deadliest assault along Egypt's tense Sinai frontier with Israel and Gaza in decades, crowds of angry mourners wept at the military funeral for the slain guards in Cairo.
Lawlessness has spread in the rugged desert Sinai 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 is yet to be tested.
Militants in Sinai sworn to destroying Israel have repeatedly attacked gas pipelines to Israel as well as Egyptian police stations and security checkpoints. Eight Israelis have been killed in border attacks in the past year.
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.
The government in Cairo said gunmen behind Sunday's attack had reached Egypt via the Gaza smuggling tunnels.
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 but also food and fuel that are a lifeline for the small enclave'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.
New Egyptian President Muhammad Mursi quickly pledged to bring the region back under government control after the attack on Sunday, the worst since Egypt made peace with Israel in 1979, ending a succession of wars.Political problem
But sealing tunnels will be an uncomfortable move for the new leader who has brought Egypt closer to Hamas since he came to power in June and has promised to help improve the life of Gaza residents.
Egypt's army command, which has kept broad sway over national security since Mubarak's overthrow, denounced the attackers as "infidels" who had crossed a red line, and it promised swift retribution.
Egyptian security forces began arresting suspects in the main northern Sinai town of el-Arish on Tuesday, the security source said, and officials checked names of potential suspects who were released from prison since Mubarak was ousted.
But there was little visible sign of a troop build-up in the area and people in Sinai said security at checkpoints on a main road into northern Sinai was no greater than normal.
Officials said they were still planning their next move.
"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.
Another said the absence of a quick increase in security might lure the militants behind the attack into an attempt to flee the area, and "they would then be caught by the police".
Hamas condemned the killings of the Egyptians and said it was sealing the tunnels from its side while helping Egypt to identify those behind the attack.Pressure to respond
Gunmen seized two armored vehicles during the attack and managed to barge through a border crossing in one of the vehicles into Israel where they were eventually killed by Israeli gunfire. Israel said this was a wake-up call for Egypt to deal decisively with the lax security in Sinai.
Egypt's response to the attacks will help define its new relationship with Israel.
Mubarak was a staunch US ally who cooperated closely with Israel and suppressed Islamists including Mursi's Muslim Brotherhood, which rejected violence to achieve its goals but often voiced hostility to Israel.
Israel is looking nervously for proof that Mursi will show as much willingness as Mubarak, who ruled for 30 years, to thwart the threat posed by armed religious radicals.
Relations with Israel were shaken last year by angry protests outside the Israeli embassy in Cairo that forced it to evacuate staff.
Mursi came to office in June promising to uphold peace with Israel and has kept his focus on domestic priorities up to now.
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.
The Egyptian army said 35 militants were involved and mortar bombs fired from Gaza landed in the area during the operation.
No one has claimed immediate responsibility for the attack.Flowers, flags
Mursi announced a state of national mourning and visited the scene of the attack on Monday along with top army and intelligence officials.
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 on the way for burial.
Mursi won election as the candidate of the Muslim Brotherhood but has resisted critics' efforts to paint him as its pawn, officially quitting its political party when he took office and saying he is the president of all Egyptians.
The Brotherhood on Monday blamed Israeli intelligence for the attack, an allegation that was dismissed by Israel, and one that Mursi is unlikely to champion as he tries to cement a reputation as a safe pair of hands in diplomacy.
RAFAH, Egypt (Reuters) -- Egypt began work 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 jihadi militants.