Immigration minister Robert Jenrick has drawn up a five-point plan to tackle the influx of people legally entering Britain but the Prime Minister would not confirm if he has signed it off.
Net migration into the UK peaked at 745,000 last year after official figures were revised upwards.
Mr Sunak said: “I’m very clear that the levels of migration are too high and they’ve got to come down to more sustainable levels.”
The PM pointed out that migration is now “slowing” but said he recognised “we’ve got more to go” to bring down the number of entrants.
Mr Sunak said the government has taken action this year by “clamping down on the number of dependents” that international students could bring with them to the UK.
“That action I took represents the single toughest measure that anyone has taken to bring down the levels of legal migration in a very long time,” he added.
“So that should give people a sense of my commitment to bringing migration down.”
“And if we see further abuse of the system, of course we’re prepared to act to do more.”
Mr Jenrick addressed a meeting of the New Conservatives, a group of red wall MPs on the right of the party, on Wednesday night to reassure them work is under way to reduce the numbers.
He is pushing for a ban on foreign social care workers from bringing in any dependents and a cap on the total number of NHS and social care visas.
The plan would also see the shortage occupation list scrapped, a programme that allows foreign workers to be paid 20 per cent below the going rate in roles that suffer from a shortage of skilled workers.
Former home secretary Dame Priti Patel pushed back against claims the system was being exploited.
“On the points-based system, there are very, very clear parameters as to how people come to our country,” she told TalkTV.
“We can’t just assume that people are coming here and there’s lots of free-riding taking place.”
Work and Pensions Secretary Mel Stride said the current numbers were “unacceptable”.
He suggested welfare system and tax cuts in the autumn statement could lead to a reduction in net migration by encouraging Britons into the labour market and reducing the need to fill job vacancies with foreign workers.
“We do accept that these figures are too high, they are unacceptable,” Mr Stride said.
“And that is exactly why we will be coming forward with further approaches to make sure we bring these down.
