Video report by ITV News Health Correspondent Emily Morgan
The foreign secretary said Boris Johnson would update the public later this week on "the measures and decisions that we will need to take to protect the NHS, to safeguard the economy and to avoid the risk of a second peak".
The next stage of the response will be "different", Mr Raab said, with ministers currently working out how daily life can be adjusted so there are "safe new ways to work, to travel to interact, and to go about our daily lives".
Mr Raab warned the public to "be under no illusions, the next stage won’t be easy", but he said the government hopes it will be "more comfortable".
He said experts are considering how to a formulate a "sustainable" strategy which "prevents lasting damage to jobs and livelihoods".
But he said there would be no relaxation of restrictions before the "five tests" had been met (see below).
There was also an update on the coronavirus death toll, after estimates claimed the UK had the most Covid-19 related fatalities in Europe, with32,000 victims.
Mr Raab dismissed those claims, putting UK's death toll at 29,427 - an increase of 693 from the same point yesterday.
“I don’t think you can make the international comparisons you’re suggesting at this stage, at least I don’t think you can make them reliably," he said.
He said comparisons will not be able to be made "until we’ve got comprehensive international data on all cause of mortality" and "all countries are measuring in the same way".
Despite the UK preparing to move to the next stage of its virus response, Mr Raab said the figures show "it’s not over yet".
He said releasing the wrong restrictions at the wrong time presented the “very real risk” of infection rate rising, creating the possibility of a second peak.
Testing again failed to meet the 100,000 target set by the Government, which was met at the end of April but has since dropped off.
Just 84,806 tests were carried out on Monday, Mr Raab said, however capacity is thought to be above 100,000.
With testing capacity now ramped up, the government is trying to emulate the success of the contact tracing policy adopted by South Korea.
Chief Scientific Adviser to the Ministry of Defence Angela McLean, said: "South Korea is really the place in the world that we can look to and say this works."
“It is a large country like we are. They did have quite a big outbreak actually that they brought under control with contact tracing.
“I think they are a fine example to us and we should try to emulate what they have achieved.”
Mr Raab said ministers are still considering whether to recommend the use of face coverings after the chief scientific adviser Sir Patrick Vallance said they could have a "marginal but positive" impact on reducing the spread of the virus.
Sir Patrick said the evidence is "not straightforward" and Mr Raab said ministers do not want to give "inaccurate" advice.
ITV Political Editor Robert Peston reports on the testing policy followed by the government:
“One of the things we don’t want to do is give people inaccurate advice or create false confidence or comfort in masks," said Mr Raab.
He also said ministers do not want to provoke a shortage of masks for frontline health workers by issuing the wrong advice and said a further announcement will follow “shortly”.
The first secretary also warned people about the dangers of cyber crime during the pandemic.
He said there is "clear evidence" that criminal gangs are "actively" targeting national and international organisations which are responding to Covid-19.
Criminals are "deploying Covid-19 related scams and phishing emails", most of which are intended to help gangs "steal bulk personal data".
He pointed people to advice published by the UK’s National Cyber Security Centre (NCSC) and the US’s Cybersecurity and Infrastructure Security agency (CISA).
Earlier, two of the government's top scientific advisers were quizzed by MPs on the advice given to ministers regarding several issues including lockdown, face masks and testing.
Sir Patrick Vallance, the chief scientific adviser, said it would have been "beneficial" for the UK if officials had "managed to ramp testing capacity quicker".
"For all sorts of reasons that didn’t happen," he said.
Deputy Chief Medical Officer for England Dr Jenny Harries said community testing was stopped in the middle of March because of issues with capacity.
She said: "If we had unlimited capacity, and the ongoing support beyond that, then we perhaps would choose a slightly different approach."
Sir Patrick also said decisions taken by the government in its response to coronavirus are "not led by science" as ministers often say, "they are informed by science".
In an apparent rebuke to comments often used by ministers explaining decisions, Sir Patrick Vallance told the Health and Social Care Committee that a range of options are presented at meetings and ministers are responsible for Covid-19 policy decisions.
Responding to a question about decisions made on herd immunity and when the UK went into lockdown, Sir Patrick said: "We give science advice, and then ministers have to make their decisions."
"Clearly, what we don't give advice on is absolute precise policy decisions or absolute timings," he added.
Coronavirus: Everything you need to know