Dr Lisa McNally said Sandwell was well-equipped to deal with the latest Covid outbreak, which has seen 1,730 new cases in the past week - a rise of 40 per cent.
She said extra staff had been drafted in to support contact tracing as the "last line of defence" against the virus.
However, she warned that concerns remained that the relaxation of restrictions will lead to a rise in hospital admissions, and urged people not yet vaccinated to get a jab as soon as possible.
In the weeks to July 16 the infection rate in Sandwell was the fifth highest in the West Midlands at 526.7 cases per 100,000 people. Solihull had the highest rate – and the 12th largest in the country – at 880.
Dr McNally said the spike in cases over the past week had led to the council returning to systems first brought in during the first wave of the virus, with up to 40 trained staff available to work on outbreak management and contact tracing.
She said: "People are understandably concerned about the rise in cases but I want to reassure them that we will cope with whatever the pandemic throws at us.
"We're really busy, and we are stretched, but we have never fallen over before and we won't now. One day last year we had 600 cases in one day so we know we can cope.
"We will throw the resources at any outbreak that are required to deal with it."
Dr McNally said the rising hospital admissions were a "massive worry", and appealed to the public to play their part in controlling the virus by "continuing to do things that keep them safe".
For her this involved wearing a mask and social distancing in crowded indoor areas, she said.
"This level of demand is exactly what hospitals did not need right now when they are just starting to restore services," she said.
"We haven't yet broken the link between infection and hospitalisation, and we are seeing that the vast majority of hospital admissions with coronavirus are un-vaccinated.
"It is a really dangerous decision to face these rapidly rising case rates without having had a vaccine."
Dr McNally said the borough had managed to delay the surge of the Delta variant by prioritising cases that were tested as ‘S-gene positive’ – an early indicator that an infection was a newer strain of Covid.