Julian German made the comments as Devon and Cornwall Police said the two counties are closed for Easter and that officers would be patrolling the A30 and M5 to stop anyone attempting to travel into the area from outside.
Cllr German said: “I do agree that the £60 fine isn’t necessarily a deterrent for people who can afford a second home or to come on holiday to Cornwall but that is the current power that police have and I am glad that the police are using that power and it forms part of the deterrent.
“People won’t want to be fined by the police whatever the fine is.
“Devon and Cornwall Police have been as robust as they can identifying people they believe to be on non-essential travel.
“The police are working within the legislation that has been laid out.”
The council leader again stressed that they do not want people to travel into Cornwall and they should stay at home.
He said: “We are asking visitors and second home owners to stay away from Cornwall and come back later.
“Only travel that is absolutely essential is allowed and going to second homes or on holiday does not fit into that category.”
Cllr German said the council was continuing to monitor whether accommodation providers were complying with guidelines and remaining closed to visitors.
He explained that the council had received around 650 reports and had been working to investigate those and carry out enforcement where necessary.
He said that the “overwhelming majority” of them had complied and that the council was “very grateful”.
Cllr German added: “We have a large number of elderly and vulnerable residents and we can’t risk putting extra pressure on our health services at this time.
“Stay at home and save lives.”