The Welsh Government is still finalising details of the new regulations, but Mr Drakeford told ITV News that people from high-prevalence areas of coronavirus would still be allowed to travel into Wales for work. This is created to prevent the spread of infection within Wales and to other areas of the UK.
"There has been no formal response from [PM Boris Johnson] to my requests to restrict travel into Wales from coronavirus hotspots", First Minister of Wales Mark Drakeford tweeted on Wednesday.
The comments came as Welsh Secretary Simon Hart waded into the row, warning that restrictions on travel for those in coronavirus hotspots elsewhere in the United Kingdom risked "division and confusion".
Sir Keir added: "The prime minister just needs to be clear that people shouldn't travel from high infection rate areas into areas in Wales where there aren't those high infection rates".
"I never wanted this to become an issue of the border and people travelling in and out of Wales".
Mark Drakeford said officers will be able to apply practiced techniques developed earlier in the year, when people could not travel further than five miles in Wales.
"He is frustrated. He's been asking the prime minister to work with him on this".
"We've had to use our own powers to fill that gap".
"There are exceptions as there are in the counties of Wales which are now in local lockdowns".
The chief executive of the Welsh NHS, Dr Andrew Goodall, said he would also "welcome any actions that help us have a control of the levels of community transmission" when asked if he was in favour of the travel ban.
Plaid Cymru leader Adam Price has also welcomed the Welsh Government's plan, saying the announcement was "long overdue" and necessary to protect people in Wales.
However, Paul Davies, leader of the Welsh Conservatives, called on the Welsh Government to publish supporting evidence to justify a ban on people from areas of the United Kingdom with high levels of coronavirus from coming into Wales.
Speaking at the Welsh Labour Together online event on Thursday, Mr Drakeford said: "It's thrown a spotlight onto our relationship with the UK Government, which as I've said many times, have not been what they need to be".
"They ought to sit down with everybody, look at it seriously and then make a proper decision", he said.
He explained: "We have other measures in place already, which may be helping us to begin to turn the tide".
The restrictions are expected to come into force from 6pm on Friday, and immediately prevent travel from areas in England in tiers two and three, the central belt of Scotland, and the whole of Northern Ireland.