A second Cymru Premier team has spoken out over the FAW's plans for a revamped Welsh League Cup.
The governing body announced on Monday that the four EFL clubs in Wales had agreed to play in the competition alongside the twelve Cymru Premier clubs.
But Barry Town United responded to the announcement by saying it had not given its "unequivocal support" to the changes, despite the FAW claiming the Welsh top flight's teams had given their full backing.
According to Caernarfon Town, no official vote has been held regarding the cup competition, nor the wider Proseict Cymru proposals.
In a brief statement on Tuesday, a spokesperson said: "We wish to make it clear that while the club is open to receiving more information regarding the initiative, as far as we concerned, no official vote has been taken about it nor the proposed new Welsh League Cup."
"We will not be making any further comments about Proseict Cymru nor the League Cup until we receive definite details from the FAW of what it will all look like."
Currently, the competition - known as the Nathaniel MG Cup - involves all 44 teams from the Cymru Leagues along with a number of wildcard entries, which this season, have included the U21 teams from Cardiff City, Swansea City and Newport County, along with Merthyr Tydfil.
The 'Proseict Cymru' plans would see the league cup reduced to sixteen teams - including the twelve Welsh top-flight teams and the four Welsh clubs from the EFL, including Wrexham, with second-tier clubs from the Cymru North and the Cymru South no longer involved.
In return, the EFL clubs would no longer be able to qualify for Europe via any of the English competitions - such as in 2013, when Swansea reached the Europa League after winning the League Cup.
The FAW says the new competition, which could start as early as next season, would generate an extra £3 million per season to be spent on grassroots infrastructure, women's football and both tiers of the men's Cymru Leagues.
But the involvement of the four EFL teams would still need approval from the Football Association in England.
Chief executive Noel Mooney said: "This will be a gamechanger for the development of the game as we work to unlock the full potential of Welsh football."
"It will unite Welsh football, improve the game at all levels, and deliver meaningful societal benefits across Wales making our clubs and communities more sustainable."
But Barry Town United said it was led to believe the proposals for the league cup were still in an exploratory when the FAW met with the twelve Cymru Premier clubs in September.
A spokesperson for the club said: "We are awaiting more comprehensive information and responses to the questions we have raised, which we will share with our members once clarified."
They added: "We recognise that this matter is likely to spark considerable discussion within the club, and we welcome all questions or concerns to be directed to David Cole (club secretary) via email. As more details are made available, we will organise a members' meeting to engage in a full and open debate on the proposal."
When Bro Radio News approached the FAW for a response to Barry's statement, the governing body declined to comment.
Meanwhile, the chairman of Swansea City has tried to allay concerns that the EFL clubs in Wales would gain a financial advantage over rival clubs.
Andy Coleman told BBC Wales Sport: "The important thing to note is that this was structured very intentionally in a way not to give any of the Welsh-based EFL clubs a financial advantage."
"This is meant to be a level playing field for all as we do this, with just good intentions about improving the system in Wales."
"We've given the FA a board a tap-in. This is a really good opportunity to show that football can take care of football and make common sense decisions for ourselves that strengthen the game."
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