The Commons leader, Jacob Rees-Mogg, has complained about what he called “this endless carping” about current shortages of coronavirus tests, prompting Labour to accuse the government of being out of touch with public concerns.

Responding to a question in the Commons about tests from his Labour shadow, Valerie Vaz, Rees-Mogg said there should be more praise for how well the system was doing.

“The issue of testing is one where we have gone from a disease that nobody knew about a few months ago to one where nearly a quarter of a million people a day can be tested, and the prime minister is expecting that to go up to half a million people a day by the end of October,” he said.

“And instead of this endless carping, saying it’s difficult to get them, we should actually celebrate this phenomenal success of the British nation in getting up to a quarter of a million tests of a disease that nobody knew about until earlier in the year.”

In a subsequent Labour statement, the shadow public health minister, Alex Norris, said that rather than seeking to improve Covid testing, “the government has instead resorted to a blizzard of blame-shifting and excuses”.

Norris said: “Now, out-of-touch ministers have got a new message to those who can’t get tests: stop complaining and praise us. Jacob Rees-Mogg should immediately apologise. Whining about the public not being grateful enough won’t sort anything – only his government can fix the testing shambles they are presiding over.”

The government has acknowledged difficulties with the testing system following days of reports about people being sent hundreds of miles for a test, or being unable to access one at all. Addressing a committee of MPs on Wednesday, Boris Johnson said the system currently “has huge problems”.

Nonetheless, Rees-Mogg’s comments were not very different to the previous stance taken by ministers, and by Johnson, about complaints over testing.

During prime minister’s questions a fortnight ago, after Keir Starmer focused on problems with tests, Johnson accused the Labour leader of “carping”, saying he was undermining public faith in the system.

Rees-Mogg does, however, have a reputation for insensitive remarks. Last year, he apologised after widespread criticism over comments in the Commons where he said victims of the Grenfell Tower had not used “common sense” as they did not leave the burning building, instead following fire service advice to remain in their flats.