The equivalent of 11.7 new Covid-19 cases per 100,000 people were detected in Leeds in the seven days to June 28 - the 24th highest rate of any local authority in England.
But that figure has dropped to 8.6 cases per 100,000 people over the last seven days, which is lower than the average rate in Yorkshire and the Humber.
Leeds Council said the city is unlikely to see any additional lockdown measures imposed while the rate of new cases is falling week-by-week.
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A council spokesperson said: "The current situation in Leeds is very different to that in Leicester.
"The number of cases being confirmed in Leeds has been in decline over the past week with our current rate being 8.6 cases per 100,000 of our population, which is lower than the average rate in Yorkshire and the Humber.
"By comparison, over the past 7 days, the number of cases per 100k population in Leicester was higher at 135.7, with no sign of any fall in these levels, unlike in Leeds and other parts of the country.
"This is why additional measures are being introduced in Leicester.
"We will continue to closely review the data for Leeds and advise on any measures that become necessary, but the measures currently in place are sufficient at this time.
"We continue to encourage all Leeds residents to follow the social distancing advice closely and seek a test if they have symptoms."