Protesters have been gathering outside a hotel in Newquay where asylum seekers are staying.
A controversial protest against their presence was organised to take place from noon today.
But so far counter-protesters chanting slogans such as "Refugees are welcome here" outnumber protesters.
Police at the scene have said they have resources in place for anything that happens. Similar protests elsewhere have led to confrontations and arrests.
One of the protesters, Rob Gilbert, from Goonhavern, said: "I am here supporting locals. The Government should have sorted this out before it came to this.
"We have a lot of problems in this country. We need to help our own and when we've got to a decent level we can have people come in to this country but they have to be checked."
Shaun Bishop said: "The protest is in the wrong place - it should be at the Foreign Office. Local residents should have the right to protest because people are being followed around. All they are doing is looking after their children."
But counter-protesters are insisting Cornwall should welcome refugees.
Beresford Lee said whether asylum-seekers came from the Ukraine or from other countries, they should be treated equally: "We should welcome them all."
Natasha, who did not give a surname, said: "Cornwall has chosen to welcome people from outside historically and we should stand by that."
Bill, who also did not give a surname, said: "I'm here because the issue of women being followed has turned in to a racist agenda.
"This has to be called out for what it is: it's disgusting. People are here not by choice - they've been persecuted."
Claims that women and children have been followed, allegedly by asylum seekers, have been a driving factor in the staging of the protest, the organisers of which have said they are not linked to far right groups.