The spokesperson said, "The prime minister is fully committed to bringing overall numbers down. We're considering all options to make sure the immigration system is delivering."
The opposition Labour Party said the figures showed the government had mismanaged the immigration and asylum systems and "completely failed to get a grip".
Why the net migration is record high?
Citing the reasons, the Office for National Statistics (ONS) explained a recovery of travel following COVID-19, and an increase in arrivals of international students who had been studying remotely during the pandemic had contributed to the rise.
An estimated 1.1 million long-term immigrants arrived over the period, up 435,000 on the previous year. The biggest proportion of those leaving Britain were EU nationals.
Three new visa schemes - for Ukrainians, Afghans and Hong Kong British nationals - together added around 138,000 to the number of arrivals.
"A series of world events have impacted international migration patterns in the 12 months to June 2022. Taken together these were unprecedented," Jay Lindop, Director of the ONS Centre for International Migration, said.
"Migration from non-EU countries, specifically students, is driving this rise," Lindop added. "The many factors independent of each other contributing to migration at this time mean it is too early to say whether this picture will be sustained."
How the Sunak government is tackling the situation?
Migration levels have been in the headlines again in Britain in recent weeks as some business leaders called on the government to liberalise immigration to help boost growth. That was rejected by Sunak who instead emphasised the need to tackle illegal immigration to build trust in the migration system.
Sunak and interior minister Suella Braverman have also come under pressure to do more to stop illegal migrants making perilous journeys across the Channel, with criticism of conditions at an overcrowded processing centre in southern England and a fire bomb attack on a similar site nearby.
(With inputs from agencies)