Boris Johnson is facing questions over how a disgraged former aide who resigned amid outrage over a string of controversial past past comments came to be hired.
Party chiefs have also called for answers on how the 27-year-old, who resigned this week after his "offensive" past writings were discovered online, came to be hired to work in Downing Street.
Mr Sabisky, who once suggested enforcing the uptake of contraception to stop unplanned pregnancies from creating a "permanent underclass", announced he was standing down on Monday evening.
He said he did not want to be a distraction to the Government after previous comments made by him, including that black people had a lower average IQ than white people.
Ministers said Mr Sabisky "jumped before he was pushed" following a slew of "reprehensible" past comments, but Labour has demanded answers about how such a figure came to be employed by Downing Street.
Labour chair Ian Lavery, in his letter to Mr Johnson demanding more information on the level of vetting involved, wrote: "Andrew Sabisky has thankfully left your Government.
"However, the disturbing nature of his previous comments on eugenics, race and women, which have been well documented in the press, raise very serious concerns about your own views.
"Furthermore, there are unanswered questions about how somehow with such abhorrent views was ever considered for employment in the first place."
Mr Lavery pointed to past writings by the Conservative Party leader and asked whether the PM agreed with Mr Sabisky's views on ethnic minorities.
The Labour MP added: "Boris Johnson has serious questions to answer about how this appointment was made and whether he agrees with his vile views."
Mr Sabisky, when announcing he was quitting, described media reports about his previously-aired opinions as "mad".
But Business Minister Kwasi Kwarteng blasted Mr Sabisky's past remarks as "offensive" and "racist", and alleged the aide walked out on the Government before he could be sacked.
Mr Kwarteng told Sky News he thought the Government would be "looking at vetting processes more closely" in light of the drama.
It comes as veteran politician Ken Clarke called on Mr Johnson to rein in his chief adviser Dominic Cummings following his plan to recruit "misfits and weirdos" into Number 10.
The former Tory chancellor said the brains behind the Vote Leave campaign would would only last in the job if his "personal appearances stop" and he goes back to being a "back room operator".
Mr Cummings made headlines before the Cabinet reshuffle when, in tongue-in-cheek fashion, he told broadcast reporters that cartoon superheroes would do a better job than Mr Johnson's then-current crop of close circle ministers.
"PJ Masks will do a greater job than all of them put together," he said, when about the reshuffle.
But Mr Clarke told ITV News' Acting Prime Minister podcast that former chief advisers did not "dress exotically and pose for the photographers before giving, quite blatantly, briefings all over the place about what their views are on everything".
Leaving his house on Tuesday morning, Mr Cummings suggested people should read about "super-forecasters".
He told awaiting reporters: "Read Philip Tetlock's Superforecasters instead of political pundits who don't know what they're talking about."
Superforecasting is a book by Philip Tetlock on the science of prediction.
Mr Sabisky - a self-professed "geopolitical forecaster" - wrote on Mr Cummings' website in 2014: "One way to get around the problems of unplanned pregnancies creating a permanent underclass would be to legally enforce universal uptake of long-term contraception at the onset of puberty.
"Vaccination laws give it a precedent, I would argue."