Many schools in north-west England will delay reopening at least until 22 June over concerns the coronavirus infection rate is on the rise.
Schools in Blackburn said they would not reopen on Monday, as the government has urged, while Tameside Council "strongly" advised schools not to do so.
Wirral Council also urged schools to "pause and consider" reopening plans.
Health Secretary Matt Hancock said "there is a challenge" in the region.
Some scientists say the R number is creeping up across the country and may have surpassed one - the point at which the epidemic takes off again - in the region.
Data from Public Health England, released on Friday, gave an R value of 1.01 for the North West and 1.0 for the South West, with all other regions below 1.
If the R is one or higher, the virus will spread exponentially through the population, while a value less than one indicates the virus is in decline.
Colin Cox, director of public health in Cumbria, also warned on Friday people should not be "complacent" and lockdown restrictions could be tightened if the number continues to rise.
Dr Jeanelle de Gruchy, Tameside council's public health director, has written to all head teachers "to strongly advise them to delay the wider reopening until there is further assurance that the Covid 19 infection rate is reducing".
In a statement, the authority said: "This follows new data published [on Friday] showing that the regional R rate has risen above 1, as well as local information that infection rates remain higher and health services are stretched."
Dr Paul Birrell, from a team at Public Health England (PHE) and the University of Cambridge, said the North West - with 4,170 infections a day - was "more worrying" compared to other regions, while the National Education Union (NEU) also raised concerns on Twitter.
With #R above 1 in the NW; test, track, trace, not fully operational; the increased #COVID19 risks to public health mean local councils & DPHs are advising schools to delay their wider reopening until at least 22 June. #OnlyWhenItsSafe #FiveTests @dr_sakthi @BWDDPH @DrRajpura pic.twitter.com/dv3jY46obS— Preston NEU (@Preston_NEU) June 6, 2020
The government has suggested an introduction of "local lockdown" measures to fight any flare-ups in particular areas.
But Greater Manchester Mayor Andy Burnham questioned whether such measures are workable, calling them a "recipe for chaos".
Both he and Liverpool City Region Mayor Steve Rotheram have said lockdown restrictions were being lifted too soon and were driven from London, with other regions not being listened to.
Councils in Gateshead, Hartlepool and Liverpool announced in May that they would not reopen schools on 1 June as advised by the government.
Wirral Council Leader Pat Hackett also urged people to "stay at home as much as possible" after popular areas were "jam-packed" with visitors during the warm weather last weekend.