Hamas previously condemned the killing of Ayatollah Ali Khamenei on the first day of the war as a "heinous crime", openly acknowledging his longstanding support for the Palestinian movement.
Under the first phase of a US-sponsored ceasefire in Gaza, the Israeli army withdrew to positions behind a so-called Yellow Line, but still controls over half of the territory.
Hamas recently completed the formation of a new Shura Council of more than 80 members, a consultative body largely composed of religious scholars, as well as a new 18-member political bureau.
The Islamic Group condemned the seizure, saying it was part of Israel's daily attacks and violations of Lebanon's sovereignty. It called on the Lebanese state to work for the release of Atwi.
Rifaat's role in a February 1982 massacre as part of a crackdown on an armed revolt by Islamist group the Muslim Brotherhood earned him the nickname 'the Butcher of Hama'.
