Mr Yousaf also wished a “full and speedy recovery” to a policeman injured by a firework thrown during the marches through the city centre by A Cairde Na Heireann (Calton Republicans) and the Friends of Irish Republican Prisoners Welfare Association.
About 1,000 demonstrators and counter-protesters took to the streets, resulting in 10 people being arrested for a variety of offences.
The policeman who was struck by a pyrotechnic was taken to hospital for treatment, with Assistant Chief Constable Bernard Higgins saying he was “disgusted at the recklessness and stupidity” of the protesters throwing fireworks and flares.
Mr Yousaf said: “I am very grateful to all of the officers and police staff involved in the robust policing operation around two processions in Glasgow this afternoon.
“I hope the officer injured as a result of a pyrotechnic thrown during the event will make a full and speedy recovery.”
While recognising the right to hold processions and demonstrations as “central to our democratic society”, Mr Yousaf said: “It is important that we do not lose sight of the collective need for action to achieve a zero-tolerance approach towards sectarianism and offensive behaviour.
“Scotland’s communities also have a right to feel safe and to be protected from disorder and thuggery.
“At my meeting with the city council and police on Thursday, we discussed a range of issues, including approaches for the future, including potentially allowing the council to reduce the number of marches.
“I told the council leader that we are open to considering all options, including looking at the potential for changes to legislation and guidelines should these be necessary. We’ve decided to meet again to explore all options.”
The decision to allow the marches to take place was made by SNP-run Glasgow City Council following advice from Police Scotland – despite a similar march descending into violence the previous weekend.
Mr Higgins said: “We had significant resources deployed throughout Glasgow city centre as these public processions took place.
“The majority of those who took part in the processions listened to us and complied with our instructions.
“A significant number of those who attended as part of the counter-protests were intent on stopping the processions from taking place but were prevented from doing so by prompt and decisive police action.
“I am, however, disgusted at the recklessness and stupidity of those who decided to throw pyrotechnics, one of which injured an officer.
“He was simply carrying out a duty which allows us to facilitate people’s rights and ultimately we were here today to keep everybody safe.”