A meeting to discuss military support for Hull has been held over what is being called the city's "Covid-19 emergency".
Hull continues to have the worst infection rates in England, with 748 cases per 100,000 people in the seven days to 15 November.
The gathering, between council leaders, MPs and the government's Covid-19 taskforce, was described as "positive".
Leaders say it is likely Hull will be in tier three or higher after lockdown.
The city's Labour MPs wrote to the government asking for the military's help to carry out mass testing in Hull to try and help halt the rise in cases.
In a joint statement, Hull City Council leader Stephen Brady and MPs Dame Diana Johnson, Karl Turner and Emma Hardy said: "We've had a positive meeting with the government and discussions for military support are under way.
"We also made the point that we would be keen to be part of any pilot on mass vaccination with additional logistical support."
The leaders said they also discussed with the taskforce a request to allow more flexible local decision making on school closures "if absolutely required".
On Tuesday, Hull's director of public health Julia Weldon revealed that 57 of the city's 97 schools have seen closures in some year groups.
At the meeting, a case was made for extra discretionary financial support for businesses, as well as for the city council itself, the leaders added.
Earlier, Hull University Teaching Hospitals NHS Trust announced 305 people had died from Covid-19 in the city's hospital since 19 March.
The Department of Health and Social Care previously said it was providing Hull with some of the 600,000 lateral flow tests as part of a national expansion in testing.