CAIRO (AFP) - The Egyptian authorities insisted Saturday that non-violent members of ousted president Mohamed Mursi's Muslim Brotherhood movement could take part in the country's transition.

"Anyone from the Muslim Brotherhood or the non-Muslim Brotherhood who would like to come back to join the peaceful Egyptian march towards the future will be welcomed," presidential adviser Mustafa Hegazy said.

Egypt "welcomes all parties" that have not committed any "terrorist acts", he added.

Prime Minister Hazem al-Beblawi warned separately that there would be "no reconciliation with those who have blood on their hands and have broken the law".

Hundreds of people have been killed since Mr Mursi's ouster by the military on July 3 following massive demonstrations against his rule.

Mr Mursi has been detained and other Brotherhood leaders have been rounded up or are on the run.

But the army-installed government has insisted that moderate members of the Brotherhood can participate in the political process if they choose.

The authorities have however increasingly referred to "terrorists" among Mr Mursi's loyalists and speculation has swirled that the government could move to ban the Brotherhood.

The group was banned for decades, and only came to power after the 2011 uprising that overthrew president Hosni Mubarak.

"We're not into the effort of dissolving anyone or preventing anyone" from taking part in politics, Mr Hegazy insisted on Saturday.

But, he added, "whoever has been instigating violence, has been using violence, will be banned by law".