The new powers came into effect at 10:00 BST. Participants on both sides were not seen to be wearing any face coverings when the marches started.
The city centre protests follow disorder on 6 September, when police attended Eastney Marina as hundreds of demonstrators blocked roads in an attempt to stop coaches carrying 120 migrants, who had crossed the Channel in a dinghy, from leaving the city.
On Saturday, up to 500 anti-migrant protesters held Union and St George flags while some wearing Portsmouth Patriot branded clothing gathered outside All Saints Church on Commercial Road shortly before midday on Saturday.
The crowd chanted “stop the boats” as they marched to Guidhall Square.
About 300 people joined the counter-protest.
Both sets of demonstrators were kept apart by police when they arrived at the square.
Speaking before the march, Simon Magorian, of Stand up to Racism Portsmouth, described the demonstrations in Eastney as a “horrible spectacle”.
He said: “Portsmouth is actually a good functioning multi-cultural city.
“We are now organising to have the broadest possible opposition to what we see as a fascist street movement and we’re not going to allow them to get a grip on Portsmouth or any other town – this is quite terrifying.”
Among the anti-migration protesters, Pete Davies, from Portsmouth, said he had also taken part in the demonstrations at Eastney.
“They should be having them turned back to France again. It’s a safe country, there’s no war in France.
“They want to stop the benefits, stop the free housing… they don’t give nothing back to the people of the country.”
Hampshire Police and Crime Commissioner Donna Jones said: “I’m pleased that today’s protests in Portsmouth took place without major issue.
“Thankfully, we didn’t see repeated scenes of Sunday night with assaults on police officers and criminal damage to police vehicles and people’s property.”
She thanked the officers for their work and their impartial use of the power to ask people to remove face coverings.
