Spokesman said that the report was an "attempt to demonise Hamas".
"Preachers should avoid speaking of the internal affairs of Egypt", says group official.
Has stepped up a campaign against Islamist militants in the Sinai Peninsula.
Rights official says executions are imposed without fair trial.
Rami Hamdallah has accepted Abbas request, despite recent resignation.
At issue are Hamas' ties with ousted president Mohammed Morsi.
Crackdown comes after outlets covered party's relationship with Egypt's new government.
Tunnels sealed as part of campaign against the Muslim Brotherhood
Ousted leader allegedly escaped jail with help from Hamas militants.
Accused of conspiring with Hamas, Hezbollah and local militants to free future President Morsi, among others.