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Former Brexit minister Lord Frost says he left his government position because he could not support Boris Johnson's "coercive policies on Covid".
The peer resigned on Saturday, but said he had "huge admiration" for the PM who was "the right man" to lead.
Foreign Secretary Liz Truss will now take on his role as the UK's lead negotiator in post-Brexit talks.
Justice Secretary Dominic Raab said he was sorry to see Lord Frost go, but he backed the PM's Covid measures.
He added: "If we hadn't taken the measures we had to support public health, to support businesses, to support livelihoods, to support whole communities, we would have seen much more damage done."
Lord Frost was put in charge of the government's Brexit talks in June 2019 and after the UK left the EU, he continued leading negotiations with the bloc - specifically trying to resolve problems around the Northern Ireland border.
But on Saturday, he announced his resignation from the government, citing "concerns about the current direction of travel".
Speaking to reporters on Monday, the former diplomat said he and the prime minister had "never disagreed" on Brexit policy.
But he said he could not support other measures he was taking, "most recently on Covid restrictions and Plan B".
Lord Frost added: "I don't support coercive polices on Covid."
Last week, the government introduced a number of measures, including Covid passes - which require people to show proof of vaccination or a negative test before entering a large venue, such as a nightclub.
The measures were approved by Parliament with the support of Labour MPs, but 99 Conservatives voted against Mr Johnson's passport proposal - and many spoke strongly against it.
There had been some speculation in recent weeks that the government was softening on its stance on the Northern Ireland protocol and particularly the role of the European Court of Justice.
But Lord Frost really wanted to reinforce that his resignation was not about Brexit, it is about Covid.
David Frost has always been a bit of a special case in government - he went from being a special adviser when Boris Johnson was foreign secretary, then he was brought into government in a souped-up role. A kind of "special adviser-plus" position.
Then he was put in House of Lords and made a minister, but he didn't have a government department - and he was not your typical minister.
I don't think we should view him as a canary in the coalmine for other ministers who might quit alongside him. He is a special case and has quit for very particular reasons from a job that was bit more quittable.
Now his job - which some might call it the poisoned chalice - has been passed to Liz Truss.
She will have to decide if she wants to continue with the same demands as Lord Frost, or does she want to water them down?
Ms Truss will replace Lord Frost in UK-EU talks, while Conservative MP Chris Heaton-Harris has been promoted to become her deputy as minister for Europe.
But Lord Frost's departure prompted concern among some Conservative MPs, with one describing his exit as a "disaster".
And Sir Jeffrey Donaldson - leader of the Democratic Unionist Party - said: "I do think it harms the government's position when you lose your chief negotiator in these circumstances."