Speaking in his Easter message, he reminded people to celebrate in the local area and avoid any activities that could allow the virus to spread.
From this week people can meet outdoors for exercise in groups of ten from two households and six people from two households can meet in a private garden.
"As we have seen with the increase in cases after Mother's Day and St Patrick's Day there is a worrying correlation between public holidays and subsequent higher rates of infection," he said.
"The virus is still circulating in our community and that is why I am appealing to the public in Derry and Strabane to do be on your guard this Easter weekend and celebrate safely.
"The restrictions are tough on everyone but there are ways that families can enjoy the holiday safely.
"It's still Easter and you can take part in fun activities such as Easter Egg Hunts and grandparents and other family members can still leave eggs on doorsteps for children.
"You can enjoy family time in the garden or connect online and I am personally looking forward to some Easter walks with my wife and children."
The PSNI have confirmed that they will be increasing their patrols over the break to ensure people are staying within their local area while Gardai are doing the same in Donegal where cross border travel remains forbidden.
"I'd encourage everyone to take the time to get some fresh air over the break at one of our walkways or greenways," he added.
"The increase in daytime hours means that there are more opportunities to get out and about however I would urge you to do that in our local area and only travel beyond that when it is an essential journey.
"I would also like to remind the public that cross border travel for non-essential journeys is forbidden and it is still not appropriate to visit beaches or stay in holiday homes and caravans over the border."
Meanwhile details of Derry City and Strabane District Council's opening hours and services have been confirmed for the Easter holidays.
The main offices on Strand Road will close from Friday April 2nd and will reopen on Wednesday 7 April.
The offices on Derry Road, Strabane will close on Monday 5 and Tuesday April 6.
Refuse collection services will operate as normal over the holiday period, while Recycling Centres at Strathfoyle, Pennyburn and Glendermott Road will be closed on Easter Sunday and all sites will be closed on Easter Monday before operating as normal from Tuesday April 6th.
Leisure Services remain closed in line with the guidelines from the Northern Ireland Executive to limit the spread of Covid 19.
In light of the pubic's wishes to visit loved ones in cemeteries, summer closing hours of 7pm have been brought forward to Monday March 29th .
Mayor Tierney also took the opportunity to extend his best wishes to everyone over the Easter break.
"I hope everyone takes a break from their hectic schedules to spend time with their family this Easter," he added.
For further information visit the Council website at www.derrystrabane.com.