The First Minister has called on the Prime Minister to "engage" with the devolved nations in what he described as "this most difficult week".
Mark Drakeford said there has been no meeting offered to First Ministers by Boris Johnson, and claimed he had only had one "brief" phone call with him since 28 May.
It comes as the UK Government announces more local lockdowns in parts of north west England, West Yorkshire and the Midlands.
ITV News was also told a new national lockdown is being considered in England as the "last line of defence" in stopping the spread of coronavirus.
Three more Covid-19 deaths were confirmed in Wales on Thursday - the first since August.
One more death was recorded on Friday 18th, bringing the total to 1,601 in Wales.
A further 185 cases of the virus were also reported - a total of 20,233 in Wales, although the true figure is likely to be higher.
Watch analysis from ITV Wales Political Editor Adrian Masters:
During a press conference on Friday, Mark Drakeford said: "Some of the areas where changes are being made in England are right along our border, and they have an impact on us Wales, which is why we are entitled to have an opportunity to discuss them.
"I've had no opportunity to discuss with any English minister whether or not they intend to impose any travel restrictions as part of the package of measures they are introducing.
"If they are not, then there would be no restriction on people continuing to come to Wales for holiday purposes."
The First Minister added that Wales is in the same position as it was in early February - a number of weeks behind the time lockdown was first announced.
"But this is a virus that can go from being in very low circulation to very high circulation very quickly."
He also said the Welsh Government is putting the counties of Newport and Merthyr Tydfil under "close watch" as cases in those areas rise.
It has been less than 24 hours since Rhondda Cynon Taf was put under new lockdown restrictions, after a spike in cases were reported in the region.
Since 6pm on Thursday, people cannot enter or leave the county without a reasonable excuse, such as travelling for work or education.
Indoor gatherings have also been banned in the region, including for those within the same extended household, and all licensed premises must close by 11pm.
Similar lockdown measures were introduced in Caerphilly County last week, after a number of new cases were partially linked to clusters of people meeting indoors.
Despite a rise in the number of Covid-19 cases, some have reported being unable to get tested or having to travel thousands of miles to get one.
The testing system has been struggling to cope with soaring demand which has seen patients turn up at accident and emergency in the hope of getting tested.
Watch the full press conference with the First Minister: