The ceremonies were disrupted by hecklers who chanted against Egypt's new Islamist leaders, who have condemned the attack but may yet face a backlash against their plans to relax restrictions on Gaza border crossings. Gaza is ruled by the Islamist Hamas group.
Mourners prayed for the dead at a mosque in an east Cairo suburb before the coffins, wrapped in Egypt's red-white-and-black flag, were taken to a nearby square where a military ceremony led by Defense Minister Hussein Tantawi was conducted.
The military has said that 35 gunmen attacked an Egyptian border post, killing the 16 before commandeering an armored vehicle they later used to try to storm across the border into Israel. It has accused Palestinians from Gaza of aiding the gunmen, by firing mortar shells at a nearby border cross just as the gunmen were attacking.
The killers are believed to be part of a low-level Islamist insurgency that has been active in Sinai for a decade, and which is allied with al-Qaida-inspired groups of militants in both Gaza and Sinai.
Egypt's President Mohammed Morsi, a member of the Muslim Brotherhood, and Gaza's Hamas rulers come from a different Islamist political tradition than the Sinai militants. Mourners nonetheless appeared to hold them responsible for the deaths.
"The Brotherhood and Hamas are one dirty hand," chanted some of the mourners.
Surprisingly, Morsi did not attend the funeral, though he flew to Sinai on Monday to look at the border region and familiarize himself with plans to combat militancy in the area.
Prime Minister Hesham Kandil did attend the funeral and was heckled by mourners, some of whom pelted him with shoes. Others held their shoes high, pointing their soles at him in a gesture of contempt, before he was whisked away by aides.
Kandil is not a Brotherhood member, but he is a devout Muslim said by some media reports to be sympathetic to the group.
Morsi has sought to reverse ousted leader Hosni Mubarak's hardline policy toward Hamas, promising to ease the hardship endured by Gaza's 1.6 million residents as a result of years of siege by Mubarak's Egypt and his Israeli allies.
He has promised to open the Rafah border crossing — Gazans' only gateway to the outside world — round the clock and allow goods to move to and out of the coastal territory. With their shared enmity for Israel, Morsi and Gaza's rulers had appeared ready to strike an enduring alliance that could only have alarmed many in an Israel already concerned by the rise of Islamists in Egypt.
But Sunday's attack and the Egyptian military's assertion of Palestinian involvement may already have undermined that prospect. If Morsi maintains close ties with Hamas now, he could come under criticism for prioritizing the Brotherhood's agenda over the nation's interests.