The Portuguese coach said Ghana's Sulley Muntari had possibly lacked energy in Sunday's 1-1 draw with Bari because he was fasting for the Muslim holy month of Ramadan.
The statement angered an Italian Muslim leader and reports say threats against Mourinho have been posted on websites.
"If something happens to me it will be your responsibility," Mourinho told reporters ahead of Saturday's Serie A derby with AC Milan.
"The situation with Muntari is your responsibility. I know what I said. I said 'you can't criticise the decision of Muntari because it is a question of faith and religion'.
"That means I accept it, I never said Muntari must forget his faith. If someone in the Islamic community is annoyed with me, It is your fault."
On the field, Mourinho said he was pleased to sign Dutch playmaker Wesley Sneijder from Real Madrid after the champions lacked ideas in the Serie A opener at home to Bari.
"Sneijder completes my squad. I asked for a central defender, a midfielder, a playmaker and an attacker. They've all arrived," Mourinho said referring to Lucio, Thiago Motta, Sneijder and Diego Milito/Samuel Eto'o.
"It's a shame it didn't happen in pre-season, it would have been fantastic to have a month and a half to prepare ourselves. It's a team with potential. In derbys there are no favourites, often the team that is having the worst spell wins."
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