Councillor Maria Crompton, the authority's deputy leader, issued the plea after reports of 146 new cases in Sandwell – the highest overnight total to date.
It is up from a previous highest figure of 83.
Earlier this week, the Government imposed new tier two restrictions on Sandwell, as well as Wolverhampton and Walsall, where there is high rate of Covid-19 cases.
It means residents can't mix with people from outside their own household or support bubble in any indoor setting – including homes, pubs and restaurants. The national rule of six still applies outdoors. Up to six people can now meet in a garden.
WATCH: Deputy leader's plea to residents after rise in cases
Councillor Crompton said: "As we move into winter, we are seeing infection rates rise across England, we are thinking especially about our older people. Older adults are much more vulnerable to serious illness and death if infected – and it’s crucial that older people avoid the virus.
“This is something we can all help with, no matter what our age. Younger people could bring the virus into their family and pass it on to someone older and more at risk.
“Our safety messages remain true and more important than ever – stay home as much as possible, wear face coverings in enclosed spaces and maintain social distancing.
“It’s not that long until Christmas now and I’m sure all of you, like me, want to be able to be with family and friends. But for that to be possible, we must stop the spread of the virus.
“No one wants to see another spike in deaths from Covid-19. We must protect one another."
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She added: “We are already seeing a significant rise in Covid-19 patients needing critical care in our region. Please don’t take unnecessary risks because you think you’re safe.
“Please keep a safe distance from others, wash your hands regularly and wear a face covering in shops, on public transport and in other enclosed spaces.”
Meanwhile five more coronavirus deaths were confirmed in hospitals across the Black Country, Birmingham and Staffordshire on Thursday.
The new deaths, which included two at the Sandwell and West Birmingham Hospitals NHS Trust, take the toll in the region's hospitals to 2,653.
An additional 705 have been confirmed to have died in the region's care homes since the pandemic began. However data for care home coronavirus deaths is only available from April 10, meaning the full death toll is likely to be higher.