An anti-racism rally organised by campaign group Stand Up To Racism was held on Saturday in the city, with thousands of people taking to the streets.
This was interrupted by several dozen far-right demonstrators clad in black, including at least one who made Nazi salutes. One arrest was made.
Dr Kelly said he blamed rhetoric from political parties for inciting people, and he rejected the idea the demonstrations were a result of concerns over immigration not being discussed.
He said consideration should be given to banning the marches – including the likes of the Stand Up to Racism event -entirely, as he believes they encourage far-right demonstrators to behave disruptively.
“The issue [of immigration] is well aired. I reject the idea that by preventing these disruptive marches you are in any way interfering with free speech…
“Glasgow’s reputation has always been as a welcoming city, as a city that does want to integrate. We have had other social problems before, but this is a key one at this stage and it must be a priority for everybody.”
Footage of a knife attack on Ogilvie in north Belfast on Monday night was shared widely across social media.
Alodid, 30, who is originally from Sudan, was later charged with attempted murder.
In parts of Northern Ireland, hundreds of masked people took to the streets and violence followed.
The disorder was restricted to pockets of Belfast and other towns, but across Northern Ireland schools and shops closed early, and public transport shut down.