But it added that GP practices across the region are "still asking patients to consider delaying contacting their practice unless they really need to for the next few days to allow time to clear backlogs caused by the cyber-attack".
"We are planning to continue as we have today but can not confirm when our computers will be back working".
The National Cyber Security Centre has been coordinating the State's response to the threat from the fast-spreading malicious software and has issued a series of advisory notices to Government departments and agencies.
In Australia, Alistair MacGibbon, special advisor to Prime Minister Malcolm Turnbull on Cyber Security, said some small businesses would likely be hit "but as a whole of nation we can be confident, so far, that we have missed the worst of this".
United Lincolnshire Hospitals Trust has said all patients should attend their booked outpatient appointments and operations "as planned tomorrow (Tuesday) after 'significant progress" has been made in restoring IT systems following Friday's cyber attack. Not that ransomware attacks tend to be the subject of reporting - there is quite a high rate of payment of affected users as the pricing is deliberately cheaper than most alternatives unless your back-up process is very good.
"Patients are no longer being diverted away from hospital accident and emergency units", Anne Rainsberry, NHS England's national incident director, said in a statement.
Services are returning to normal, but some places are still having problems.
"Since the global coordinated ransomware attack on thousands of private and public sector organisations across dozens of countries on Friday, there have been no sustained new attacks of that kind".
Devices across Barts Health NHS Trust, which runs the Royal London and four other east London hospitals, were marked with red tape by IT staff as they battled to get systems online.
The cyber attack that crippled NHS computer systems is the biggest of its kind ever launched, security chiefs have said.
"We haven't ruled out that this is a state attack", said Bossert.
The organisation also recommended that trusts ensure security software patches were up-to-date and that up-to-date virus software was also being used.