Downing Street has come under intense pressure to say whether it vetted a No 10 adviser who argued that intelligence is linked to race, amid fresh questions about chief aide Dominic Cummings’ drive to employ “misfits and weirdos” to work under him.

A day after Andrew Sabisky said he would step down as a “contractor” to Downing Street because of the furore about his posts online, Labour wrote to Boris Johnson asking him to explain how the appointment was made, and whether the prime minister agreed with Sabisky’s views.

The business minister, Kwasi Kwarteng, who was sent to speak to broadcasters on behalf of the government on Tuesday morning following the adviser’s exit, called for the process for hiring staff to be “looked at”.

Separately, a Labour MP wrote to the head of the civil service, Mark Sedwill, requesting information on who hired Sabisky and whether he was vetted.

However, No 10 refused to respond to separate questions from the Guardian about Sabisky’s employment, whether he was vetted or had a security pass.

Downing Street has so far declined to give even basic details of Sabisky’s work, or how he was recruited. Officials also refused to comment on the status of two other so-called “super-forecasters” pictured with him outside No 10 in January.

The photo was tweeted by Michael Story, co-founder of a forecasting startup called Maby, who has now made his Twitter account private. It showed Story and Sabisky with the other founder of Maby, Thomas Liptay.

Sabisky stepped down following increasing criticism from Conservatives and opposition politicians after details emerged of his views on subjects ranging from black people’s IQs to using brain-enhancing drugs on children, and whether benefits claimants should be encouraged to have fewer children.

The Labour chair, Ian Lavery, wrote to Johnson asking about how Sabisky was hired, whether he was vetted, and if the PM approved the process. Lavery also asked whether Johnson agreed with Sabisky’s views on race and intelligence, and other subjects. Downing Street officials refused to comment on this on Monday.

Separately, Labour MP Stephen Doughty has written to Sedwill seeking answers on a series of issues connected to Sabisky, including the basis on which he was hired, who approved his employment, whether the Cabinet Office was informed, and any vetting which took place.

No 10 did not respond to questions on whether Story and Liptay worked at Downing Street or had been offered work.

The SNP also demanded Johnson say whether Sabisky was vetted, arguing that the prime minister had “serious questions to answer” over the appointment.

Kirsty Blackman, the party’s deputy Westminster leader, said: “It is beyond shameful that a man with a well-documented history of unapologetically offensive, misogynistic, and racist remarks was considered by No 10 to be an appropriate hire.

“Special advisers do not have the power to hire contractors or to appoint advisers without ministerial approval so there must now be full transparency and the Tories must set out which government minister signed off on hiring Sabisky.”

Sabisky appears to have been the first hire in response to a rambling blogpost in the new year by Cummings, Johnson’s chief adviser, calling for “weirdos and misfits with odd skills” to apply for new jobs within No 10.

As news of Sabisky’s role emerged, so did details of views he had expounded energetically over years of writing, blogging and social media comments, much of it based around a belief in genetics as the main driver for people’s life chances.

This included arguing that differences in intelligence and ability between races and social classes are largely hereditary, and thus there is little point running positive discrimination schemes or Sure Start-like early intervention programmes.

It prompted a handful of Conservative MPs to speak out publicly against Sabisky, with other government advisers left notably unhappy at the coverage. One said: “We don’t want to all be tarred with the same brush – that he is in someway representative of all spads.”

Downing Street had appeared resolute in sticking by Sabisky throughout Monday, but he abruptly left that evening amid widespread reports that he had been ordered to step down.

Kwarteng, was notably more outspoken than Downing Street officials, saying: “I think it’s unfortunate he was hired … We do need to look at these processes.”

Describing Sabisky’s views as “racist, offensive and objectionable”, the business minister told BBC Radio 5 live he was glad the adviser had left.

He said the government “should prevent racists from coming into No 10 or wherever he was working”, adding: “The fact is his remarks have been identified and very quickly pushed out … and we can move on.”