Rishi Sunak has said the UK is a "compassionate" country, after the home secretary was criticised for saying southern England was facing an "invasion" of illegal migrants.
Suella Braverman was accused of using inflammatory language by refugee charities and opposition parties.
But some Tory MPs and the ex-leader of UKIP said she was right to speak out.
Downing Street did not comment on whether the prime minister would also describe the situation as an invasion.
But Mr Sunak's official spokesman said: "The home secretary was seeking to express the sheer scale of the challenge that faces the country, with people, including a significant proportion of economic migrants, seeking to make this journey."
Ministers are under pressure to tackle the growing numbers crossing the Channel in small boats.
Ms Braverman has been criticised for overcrowding at the Manston migrant processing centre in Kent, which has reportedly led to outbreaks of disease and violence.
The prime minister's official spokesman said Rishi Sunak told his cabinet at a meeting on Tuesday that the UK would "always be a compassionate, welcoming country".
Earlier, Immigration Minister Robert Jenrick told the BBC politicians must be careful with their language when talking about this issue.
Charities criticised the use of the word "invasion", with the Refugee Council saying the language was "appalling, wrong and dangerous".
Conservative MP Sir Roger Gale, who represents North Thanet, where the Manston centre is located, said using such "inflammatory language" was "completely unacceptable" and "might well incite an unpleasant element in British society to violence".
He told the BBC's Newshour programme Ms Braverman's insistence that she had not blocked the use of hotels to ease overcrowding at Manston was "disingenuous" and the problem was made "right at the top of the Home Office".
He claimed Ms Braverman's predecessors as home secretary had commissioned alternative accommodation but she had not, leading to a "log jam".
Asked if this was a generous way of saying Ms Braverman was not telling the truth, he replied: "Yes."
Other Conservative MPs supported Ms Braverman, with Brendan Clarke-Smith saying she was "right", adding that "we must stop people abusing our system, rather than making excuses for them".
Nigel Farage, former leader of the Brexit Party and UKIP, said in a Twitter video Ms Braverman was right to use the word "invasion" and she had "the guts to say many of these people are just not refugees".
Labour's shadow home secretary Yvette Cooper said: "No home secretary who was serious about public safety or national security would use highly inflammatory language on the day after a dangerous petrol bomb attack on a Dover initial processing centre."
The SNP said Ms Braverman's "incendiary language makes a mockery of [prime minister] Rishi Sunak's claims about so-called compassionate conservatism".
At one point over the weekend some 4,000 people were being held at the former RAF base at Manston, which is only designed to accommodate 1,600 people on a temporary basis.
Hundreds of people were moved there on Sunday after a man threw firebombs at a separate immigration centre in Dover.
The home secretary told Tuesday's cabinet meeting the Dover centre had now reopened and large numbers were being taken from Manston to other accommodation.
A report from a visit by the chief inspector of prisons in July found Manston had considerably improved but still identified issues such as no access to fresh air or exercise and a lack of beds, with people sleeping on rubber mats on the floor.
Since then, chief inspector Charlie Taylor said the situation had "significantly deteriorated".
People are only supposed to be kept at Manston for 24 hours for security and identity checks, before being moved into the Home Office's asylum accommodation system, which often means a hotel.
When the chief inspector of immigration visited last week, he found some people had been there for over a month. That included one family who had been there for 32 days, sleeping on mats in a marquee.
Migrants rest at an unnamed Home Office facility in Kent
In pictures sent to the BBC, the walls in the facility are covered in writing
At another unnamed Home Office facility, in Kent, young people sleep on the floor on padded mats with only a thin blanket for warmth.
Pictures released to the BBC show their room is sparsely decorated, with just a few books and a box of Scrabble as entertainment to help pass the time in the facility.
Writing in different languages is scrawled on the walls above a row of plastic chairs, fixed to the floor.
The BBC understands the facility is used to process unaccompanied asylum-seeking children.
A record number of migrants have arrived in the UK on small boats this year, with nearly 1,000 making the crossing on Saturday, a further 468 crossing on Sunday and 46 on Monday.
The home secretary told MPs on Monday that taxpayers face "a bill of £6.8m a day for hotel accommodation" for migrants.
Immigration Minister Robert Jenrick: "We have to grip this (migration) challenge"
Suella Braverman: "There are some people who would prefer to be rid of me... let them try"