Dr Sakthi Karunanithi has warned against the reopening to Reception, Year one and Year six pupils because, in his professional view, two of the government's five coronavirus tests are not currently being met in the county.
Although the number of new cases has fallen, Lancashire and the North West has a high number of cases compared to many other regions in the country.
And, although the weekly death count in Lancashire is showing a downward trend, a consistent decline is not being seen in all areas, and in recent weeks we have seen an increase. It has also been widely reported that the R value for the North West is above One.
The county says There has been positive work between local organisations to plan for outbreaks in Lancashire, but better they need information sharing from the national to local level .
Lancashire people have worked so hard throughout the epidemic in keeping the virus at bay. With various national lockdown measures lifting, we need to remain vigilant in following social distancing rules to help prevent the infection spreading.
The guidance, which also applies to early years settings such as nurseries and childminders, will be reviewed again on June 15.
The decision whether or not to admit more pupils to Lancashire's schools lies with head teachers, in consultation with their board of governors, taking into account their individual circumstances.
The county council works closely with schools to provide advice and support and all schools are encouraged to admit vulnerable pupils and those of key workers as long as their risk assessments suggest it is safe to do so.
Dr Karunanithi said: "I have carefully considered all of the information and data and, for now, my advice remains unchanged. Although there are significantly fewer numbers of cases currently, I am concerned about the high level of infections in the county when compared with others parts of England.
"The death rates are not sustainably decreasing in the county, and reports that the R value is above 1 in the North West should be an early warning sign. It is important to stress that the R value is only one part of the overall picture, it appears to be rising in most parts of Lancashire."
But he added: "We still need better information sharing from national colleagues to help us unlock a successful test and track programme, although agencies are working well locally.
"Ultimately we all have a role to play in this – we must follow social distancing rules, practise good hand hygiene, and stay at home if we have a cough, fever, loss of smell or taste or when asked to do so by the contact tracing programme. If we all play our part – national government, local partners and the public – we can contain this virus."
County Councillor Phillippa Williamson, cabinet member for children, young people and schools, added: "Everyone wants to see children back in school as soon as it is safe for this to happen and, although we are seeing some progress, we must support the professional judgement of our public health experts.
"Throughout this crisis our schools have been open to the children of key workers and vulnerable children and have also done a fantastic job in keeping in contact with parents and pupils and providing high quality online learning tools."
County Councillor Shaun Turner,cabinet member for health and Wellbeing, added: "It is really encouraging that we are making progress with the local implementation of the NHS Test and Trace system. We will continue to raise with government the need for local experts to be better embedded into the national programme.
"The vast majority of Lancashire people have been magnificent throughout this crisis, but we all have a responsibility to continue to abide by the social distancing rules. There can be no let-up because if we all play our part we can stop coronavirus in its tracks and ultimately save lives."
For the latest information on schools, read theschools coronavirus webpage at www.lancashire.gov.uk/coronavirus-updates/schools/