Councillor Patrick Harley said he would "absolutely oppose" any attempt to move the borough into Tier 3 with the rest of the West Midlands.
The Dudley and Staffordshire boroughs were today moved up from "medium risk" Tier 1 into "high risk" Tier 2 - the same tier as Walsall, Wolverhampton, Sandwell, Solihull and Birmingham.
And yesterday it was confirmed that discussions would begin in earnest next week regarding moving parts of the region into Tier 3 as infection rates continue to rise.
However it has since emerged that the Government is now considering implementing a new national lockdown for England from as early as next week.
Latest Covid-19 infection rates in the region
The latest rolling seven-day infection rate of Covid-19 by local authority area, compared to the previous week.
The figures are for the seven days to October 26, with data for the most recent four days (October 27-30) excluded as it is incomplete and does not reflect the true number of cases.
The rate is expressed as the number of new cases per 100,000 people.
From left to right, it reads: name of local authority; rate of new cases in the seven days to October 26; number (in brackets) of new cases recorded in the seven days to October 26; rate of new cases in the seven days to October 19; number (in brackets) of new cases recorded in the seven days to October 19.
South Staffordshire 401.1 (451), 237.5 (267)
Cannock Chase 343.4 (346), 230.2 (232)
Walsall 336.3 (960), 235.0 (671)
Sandwell 317.9 (1044), 223.5 (734)
Stoke-on-Trent 315.9 (810), 221.6 (568)
Birmingham 276.4 (3156), 240.6 (2747)
Dudley 260.6 (838), 163.9 (527)
Wolverhampton 251.0 (661), 197.8 (521)
Stafford 243.3 (334), 162.4 (223)
Lichfield 234.8 (246), 164.2 (172)
Solihull 229.2 (496), 225.5 (488)
Telford and Wrekin 219.6 (395), 168.5 (303)
Shropshire 135.5 (438), 87.3 (282)
Councillor Harley, a Conservative, said Dudley needed to be given "ample time" to see whether the new Tier 2 measures could bring the Covid-19 case rate down before Tier 3 should be considered.
He said: "I absolutely oppose any attempt to take us into Tier 3 along with my cabinet – we will not support moving Dudley into that tier.
"For the record, I don't like us being in Tier 2. I think it would be ridiculous to put Dudley in with the rest of the West Midlands when it's only just been announced we're going into Tier 2."
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Figures for the week to October 26 - the latest period with full data available - put the infection rate in Dudley at 260.6 cases per 100,000 people, up from 163.9 the week before.
South Staffordshire had the highest rate in the region at 401, with Cannock Chase, Walsall and Solihull the areas with the next highest rates.
Councillor Harley added: "There's no point in having tiers without giving them ample time for them to work. I would not support – in any way – Dudley being moved into Tier 3.
"We will do whatever we can to opposite it. Tier 2 has to be given time to work and the talk of it being moved up is foolish and clearly wrong.
"We have to be given time in Tier 2 to suppress the numbers."
Restrictions under "high risk" Tier 2 ban people from mixing with anyone from other households indoors, with Tier 3 forcing pubs and bars to close unless they serve substantial meals.
Other harsher restrictions in Tier 3 – the highest tier – include a ban on wedding receptions and people meeting anyone outside their household whether indoors or outdoors.
Walsall Council leader: Are restrictions effective?
Meanwhile Walsall Council leader Mike Bird has raised concerns over the effectiveness of Tier 3 restrictions.
Councillor Bird said the measures didn't seem to be having the desired impact in some areas, with Blackburn with Darwen in Lancashire recording the highest infection rate in the country in the week to Thursday despite being under the measures for 10 days.
Councillor Bird, also a Conservative, said it was his "biggest worry" that restrictions would be imposed on the West Midlands but not have a major impact.
He said: "With the restrictions, I don't think it will be this week but it's quite possible they come in the week after.
"My biggest worry is if you look at the Tier 3 restrictions it doesn't look like it's having the effect people would like and it bothers me – and if it doesn't we need to look at a different ball game.
"I've said the Government, in my view, need to make wearing masks mandatory. There's still supermarkets in Walsall and elsewhere that are not asking customers about wearing a mask.
"The jury is out on whether they work or not but people are falling down on the side of they are good. Something like that could bring the numbers down and it could stop us going into Tier 3.
"Tier 3 restrictions are quite severe, not as severe as a complete lockdown, but I have to stress no decisions have been made."
Councillor Bird said discussions had been ongoing between council leaders and West Midlands Mayor Andy Street to put a package in place for them to use if measures are enforced.
"At the end of the day there's a mood amongst some leaders of the seven local authorities that it's far better to negotiate what we can do now, rather than be in a situation like Andy Burnham was," he said.
"You write your will when you're still alive. If you can negotiate a deal over Tier 3 restrictions – and we all hope it doesn't come to that – then the package will kick in [if restrictions are imposed] and we all know what we're doing – we'll have advanced knowledge of it."
Wolverhampton Council leader urges vigilance
Meanwhile Wolverhampton Council's leader has urged people to carry on following coronavirus rules in a bid to prevent any further restrictions.
Wolverhampton's rate for the week to October 26 was 251 cases per 100,000 people, up from 197.8 the week before.
Councillor Brookfield: "No decision has been taken at this time to move the city into Tier 3 but we continue to closely monitor and discuss the situation with our colleagues across the region.
"In the meantime, our message is to carry on doing the simple things that can really make a difference to prevent the spread of Covid-19 like wearing your face covering, avoid household mixing and get a test if you have any symptoms."