Home Secretary Priti Patel should explain the UK's coronavirus border policy to MPs, Labour has said.
It came after Ms Patel said the borders should have been closed in March 2020 to slow the virus.
The UK did not impose a ban or quarantine restrictions on travellers arriving into the UK from abroad between mid-March and June.
Asked about her comments, Boris Johnson said the UK had "instituted one of the toughest border regimes in the world".
He also accused Labour of "looking backwards, playing politics and sniping from the side-lines".
However in a letter to Ms Patel, Labour's shadow home secretary Nick Thomas-Symonds expressed concern that "the government's chaotic border policy led to vital opportunities to stop the spread of the virus being missed."
"Conservative incompetence meant ministers were too slow to take action on securing our borders against Covid and have failed to enact a clear strategy throughout this crisis, including on border testing."
He called on the home secretary to urgently update the House of Commons "on what has been learned from these critical mistakes".
In video obtained by the Guido Fawkes website, Ms Patel told a meeting of the Conservative Friends of India group on Tuesday night that she had been "an advocate of closing them [the borders] last March".
Quarantine rules were introduced in June for all arrivals to the UK and in July "travel corridors" were introduced exempting travellers from certain countries from having to quarantine.
A report from the Home Affairs Committee of MPs previously described the failure to implement border measures earlier in the pandemic as "a serious mistake".
At the time, the Home Office insisted all government decisions had been "been guided by the science, with appropriate measures introduced at the right time to keep us all safe".
Asked about Ms Patel's comments on the call, a Home Office spokesman said: "We have strong measures at the border in place which are vital as we roll out the vaccine."