In talks with Interior Minister Ahmed Gamal al-Din, they also backed plans to destroy smuggling tunnels into Gaza.
The move comes as Egyptian troops mass in the area in an operation to contain Islamist militants who have built up a presence in the area.
The militants are suspected of killing 16 Egyptian border guards on Sunday.
Egypt has deployed extra troops, tanks and other armored vehicles.
Ahmed Gamal al-Din met the tribal leaders late on Thursday night at al-Arish, about 50 km (30 miles) west of the Gaza border, to ask for their support.
He later told reporters: “With the help of the people [of Sinai], the mission will succeed.”
Sheikh Atef Zayed, a member of Al-Rishad tribe, said all present had pledged to support the military’s operation.
“Egypt’s security is a part of Sinai’s security,” Reuters news agency quoted him as saying.
Another tribal leader, Eid Abu Marzuka, said the tribes had also reached a consensus that the tunnels should be destroyed.
“Let Hamas be upset, we don’t care,” he said, of the Islamist group which control the Gaza Strip.
Eid Abu Marzuka said Israel’s contact with Palestinians in Gaza should be through the official Rafah border crossing.
There are more than 1,200 illegal tunnels along the Egypt-Gaza border. They are used to get basic goods past Israel’s blockade of the enclave but also smuggle in weapons and people.
The militants who launched Sunday’s attacks are believed to have used them as an escape route.
Egypt’s Mena news agency reports that the army has already begun sealing them off.
The latest violence in the Sinai region began on Sunday, when militants carried out the deadliest and most brazen attack against Egyptian troops in the Sinai region for decades, killing 16 border guards.
There were further attacks on checkpoints in al-Arish on Wednesday, which left a number of people wounded.
Egypt launched its military offensive hours later, carrying out missile strikes from helicopters.
According to military officials, 20 people were killed in the village of Touma, while the Sheikh Zuwaid area to the west was also hit.
Further armoured personnel carriers could be seen overnight on Thursday, heading eastwards towards the border region.
Egypt’s military presence in Sinai is limited and requires Israeli approval under the terms of the 1979 peace treaty which returned Sinai to Egyptian control.
Analysts say that the security situation in the area has deteriorated following the fall of Hosni Mubarak last year, and that Islamist extremists appear to have gained a foothold.
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