Justice Secretary Humza Yousaf has said he is "open-minded" about increasing council powers to restrict marches on both sides of Scotland's sectarian divide.
But he said introducing a blanket ban on loyalist and republican parades would be impossible as the European Convention on Human Rights "simply wouldn't allow it".
The Justice Secretary spoke out after an Irish unity march in Glasgow last month sparked clashes.
Riot police, mounted officers, a force helicopter and dog units were used to quell "significant disorder" in Govan after a march through the area, organised by the James Connolly Republican Flute Band, was met by hundreds of "disruptive" counter-demonstrators.
First Minister Nicola Sturgeon said on Thursday the Scottish Government is considering changing the law to tackle the "scourge" of sectarianism following the violent clashes.
Mr Yousaf said he was "open-minded" about taking legislative action to increase the powers local authorities have over such events.
But he tweeted: "Those calling for a blanket ban on loyalist/republican parades must understand that ECHR law simply wouldn't allow it."
The Justice Secretary, who had discussions with Glasgow City Council about the issue on Thursday, added: "If there is something we can do legislatively to give more powers to councils to restrict these marches, I am open-minded."
Former first minister Lord McConnell claimed the SNP Government has not done enough to tackle the problem.
The ex-Scottish Labour leader accused the SNP of "closing down" anti-sectarian summits his administration had held when it came to power in 2007 and of "ending the Scottish
Government-led drive for change in sport, marches, education and work was an act of political vandalism".
He tweeted: "We are reaping the consequences now. Time for action again. Warm words are not enough.