CAIRO -- A senior figure in the Muslim Brotherhood's political party was arrested Monday on the eve of a major Muslim holiday, while the family of the organization's jailed leader issued a defiant statement saying he wouldn't renounce his claim to Egypt's presidency. As Egyptians prepared to celebrate Eid al-Adha, or the Feast of Sacrifice, which begins Tuesday, neither the Brotherhood nor the military-backed interim government showed any sign of moving toward a political compromise. Most of the Brotherhood's leadership has been in jail for months, and Egyptian authorities have been moving to systematically sweep up those who remain at large. The latest high-profile arrest was that of Walid Haddad, the head of external relations for the Brotherhood's political arm, the Freedom and Justice Party, who was seized in Cairo. The Brotherhood and all groups affiliated with it have been formally banned, and the government is moving to seize the organization's assets. Morsi, who is to be put on trial next month, still believes himself to be the country's legitimate leader, according to an Eid statement issued by his family and carried on the group's main website. Egypt's first democratically elected president, Morsi was overthrown on July 3 by the military, which said it was carrying out the popular will. The family statement said Morsi "would not retreat from the democratic path that the people chose." "The president will not back down or compromise or accept middle-ground solutions, especially after all the martyrs, the wounded, the detainees and the missing persons," it added. Nearly 1,000 Morsi supporters were killed in a mid-August crackdown on protest camps set up by those demanding his reinstatement, and about 2,000 members of the Brotherhood's rank and file are in jail. Authorities have managed to contain most protests staged by the group, but chaotic street clashes on Oct. 6 left 57 people dead. In another sign of tensions between the interim government and Islamists, Egypt announced it was closing the border with the Gaza Strip for five days surrounding the holiday. Gaza is the redoubt of Hamas, the Islamist group which Egypt accuses of colluding with Morsi to allow militant groups to ensconce themselves in the Sinai Peninsula. Egyptian police and soldiers for the past two months have been carrying out a sustained offensive in the Sinai, with casualties reported almost daily.