An Egyptian court last week banned the Izz ad-Din al-Qassam Brigades, Hamas's armed wing, in line with a crackdown by President Abdel Fattah al-Sisi on the Muslim Brotherhood, of which Hamas is an offshoot.
That decision prompted a source close to the Brigades to say that Egypt, which has mediated several past ceasefires between Israel and the Palestinians, including a truce to end a 50-day Gaza conflict last summer, could no longer be trusted as an impartial player.
In the statement read aloud by the gunman in Gaza, the 10 armed groups said that their fight was only with Israel and they had never taken the battle outside the region encompassing Israel and the territories claimed by the Palestinians.
"Resistance factions and the Qassam Brigades concentrate their work against the Zionist enemy," the gunman said.
"We reaffirm that we do not intervene in the internal affairs of Arab countries and we hope that no one will export their internal problems towards the Palestinian people and its resistance factions."
As well as the Qassam Brigades, the statement was signed by Islamic Jihad, the Aqsa Martyrs' Brigade, the Popular Front for the Liberation of Palestine, a Salafi group called Swords of Islam, and five other factions.
Egypt says that weapons are smuggled from Gaza into northern Sinai, where they end up in the hands of militant groups fighting to topple Sisi's Western-backed government.
Hamas, which has controlled Gaza since 2007, has denied providing any logistical, military or other assistance to groups fighting Egyptian troops.
Last week the Egyptian wing of Islamic State claimed the killing of at least 30 soldiers and police officers in four separate attacks in North Sinai, among the bloodiest in years.
Egypt's border with Gaza saw explosions and gunfire on Tuesday. Egyptian security sources said a Hamas bomb exploded on Gaza territory near an Egyptian army convoy, prompting troops to return fire. Hamas said Egyptian forces opened fire unprovoked.
In Alexandria a man was killed Tuesday in a bomb blast hours after two devices were discovered at Cairo airport and another went off in the centre of the capital without casualties, security sources said.