Among the Egyptian delegation was presidential adviser for foreign affairs and international cooperation, Essam el-Haddad, and the head of Egypt’s intelligence services, Mohammed Rifaat Shehata.
A statement from Egypt's president said one of the envoys Haddad was carrying a letter from President Mohammed Mursi to the UAE President Sheik Khalifa bin Zayed al-Nahyan.
Mursi is from the Muslim Brotherhood, which has emerged as Egypt's most powerful political force in the aftermath of the uprising that ousted longtime President Hosni Mubarak nearly two years ago.
The statement did not disclose the contents of the letter. It said Haddad would also meet officials in Dubai and Abu Dhabi.
The UAE's al-Khaleej newspaper reported Tuesday that the 11 Egyptians were arrested last month after allegedly collecting security information about the UAE, holding secret meetings, recruiting members and sending large amounts of money to Brotherhood leaders in Cairo.
Envoys are expected to discuss relations between the two countries, which have soured after Egyptian presidential candidate and former Prime Minister Ahmed Shafiq flew to the UAE soon after he narrowly lost to Mursi in Egypt's presidential elections last year.
Litigation against Shafiq followed his departure, with a number of investigations and court cases accusing him of corruption during his long political career under Mubarak.
In September, Dubai's police chief, Lt. Gen. Dahi Khalfan Tamim, warned of an “international plot” to overthrow the Gulf governments by Islamists inspired by the rise to power of the Muslim Brotherhood in Egypt.