In the letter, the leaders said there was “evidence of a flattening of the curve” and “there is a collective view – we can make Alert Level 2 work.”
Gateshead Council chief Martin Gannon confirmed the government had agreed to give the region one more week before a decision was made.
He said: “The data shows a significant slowdown over the past week. The government admits that we need a little more time to prove this trend.
“Now we have to ask everyone to help us, thank you to those who won us this reprieve.
“We are looking at the barrel of a gun, it is a battle to prove that we can do it, to save the economy and the jobs. “
This comes as Lancashire has been placed in level 3, which means the shutdown of the county’s leisure industry.
At present, Greater Manchester leaders are in talks to resist measures imposed across the region.
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In the letter, the leaders urged the government to allow more time for the current restrictions and warned that the economic consequences would be “devastating without additional support.”
The authorities have also stated that more financial support is needed for these areas at Levels 2 and 3.
They warned that paying two-thirds of wages “would not be enough to protect the jobs of thousands of people” and that payments to employees of companies forced to close should at least match 80% of the initial leave program.