NHS Highland made the appeal after more than 700 cases across its catchment area, which includes Argyll and Bute, since Christmas Eve.
Residents have been encouraged to continue following guidance on social distancing as well as other areas of government guidance.
Scotland was placed into a second national lockdown by First Minister Nicola Sturgeon on Monday January 4 after a sharp rise in positive cases across the country.
Dr Ken Oates, NHS Highland public health consultant, said: 'Firstly, thank you so much for all your support so far. We recognise that 2020 was an extremely challenging year for everyone and that we all have made significant sacrifices to reduce the spread of Covid-19 cases as much as possible.
Dr Oates reported a significant increase in case numbers in the NHS Highland area over recent weeks.
He added: 'We believe that this is due to pre-Christmas socialising, combined with people mixing indoors over the festive period.
'This has led to many extended family clusters and we would once again encourage people not to mix with others outside your household, as this is driving up infection rates.
'This has a detrimental effect on NHS services as well as the health and wellbeing of some of the most vulnerable people in our communities.
'Covid-19 will spread rapidly if given the opportunity, especially with the new strain which spreads much more easily.'
The warning came as a Loch Fyne-side GP practice informed patients of a 'significant local outbreak of Covid' in the community.
Strachur Medical Practice posted on social media that local hospitals were 'under extreme pressure', adding that 'the current situation is extremely serious'.
Dr Oates advised: 'We appreciate how challenging this has been for many people, however, when the number of cases of Covid-19 rises in our communities, we inevitably also see an increase in positive cases in health care workers and care home staff.
'We must all take action to protect each other and the NHS across Highland, Argyll and Bute. Please continue to follow the national guidance on Covid-19 including isolating at home if you feel unwell in any way, and seeking a Covid-19 test.'
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