Households in the UK will be offered £350 a month to open their homes to people fleeing the war in Ukraine.
The government’s Homes for Ukraine scheme calls on people to offer a spare room or an empty property to a refugee for a period of at least six months.
But the Refugee Council said it was worried about the level of support for people traumatised by the war.
Labour said there many unanswered questions, and accused the government of “dragging its feet” over the crisis.
More than 2.5 million people have fled Ukraine because of Russia’s invasion, in what the UN has called the fastest-growing refugee crisis since World War Two.
The government has faced criticism – including from its own MPs – over the speed and scale of its response.
The first ministers of Scotland and Wales have written to the Westminster government to propose that their nations go further, acting as “super sponsors” to offer temporary accommodation to refugees and enable them to come to the UK faster.
Announcing the new scheme, Levelling Up Secretary Michael Gove urged people to join the “national effort” and give a safe home to those in need.
Individuals acting as sponsors will be able to nominate a named Ukrainian individual or family to stay with them rent-free in their home, or in a separate property, for six months.
Sponsors won’t be required to know them in advance – they might find them, for example, through posts on social media.
There will be no limit on the number of refugees who can come to the UK through this route, and they will be given three years leave to remain, with the right to work and access public services.
Applications would be made online, with both sponsors being vetted and refugees having to go through security checks. The sponsor would get a “thank you” payment of £350 a month.
A website for people to express an interest in offering accommodation will launch on Monday.
In a later phase, organisations such as charities and churches will be able to do the same, though there is no start date for this yet.
Announcing the plan, Mr Gove said: “The crisis in Ukraine has sent shock waves across the world as hundreds of thousands of innocent people have been forced to flee their homes, leaving everything they know and love behind.
“The UK stands behind Ukraine in their darkest hour and the British public understand the need to get as many people to safety as quickly as we can.”
But the Refugee Council – a charity supporting refugees and asylum seekers in the UK – said it was concerned that people from Ukraine were facing further “bureaucratic hurdles”, and said the government scheme fell short of what was needed.
Chief executive Enver Solomon said: “We are concerned that people from Ukraine are still not being recognised as refugees and being asked to apply for visas when they just need to be guaranteed protection.”
Claiming formal refugee status, or permission to stay for humanitarian reasons through the asylum system, does not require a visa and allows an applicant and their dependants to stay in the UK for five years, with the right to work, study and apply for benefits.
He said that the sponsorship scheme “will inevitably be restricted to those who are known to people in the UK and be a quite complex lengthy visa application process”.
Mr Solomon said there were also concerns about the support available to sponsors.
“We are talking about very traumatised women and children whose experiences are unique, and the level of support needs to match that,” he said.
“It’s like asking people to be foster carers without any robust checks, training or having a social worker in place to support them.”
Labour’s Lisa Nandy said it was unclear what support would be offered to vulnerable children and older people, whether provision would made for unaccompanied children, and what help would go to local government, sponsoring organisations and housing providers.
Scotland’s First Minister Nicola Sturgeon and her counterpart in Wales, Mark Drakeford, called for all visa requirements for Ukrainian nationals to be waived and urged the government to provide more clarity on how the scheme will work.
They said becoming “super sponsors” would allow the two nations to take refugees more quickly and give them access to safeguarding and services while a longer-term sponsor is found.
The most recent figures show only 1,000 refugees have been granted UK visas – and only those with family connections have been able to make an application, via the Ukraine Family Scheme.
More than 20,000 Ukrainians have begun applications and Prime Minister Boris Johnson suggested the UK could take in 200,000 refugees.
The European Union is allowing Ukrainians three-year residency without a visa, but the UK says controls on entry are essential for security.