A Brexit minister should be appointed to put Wales' interests "at the centre" of negotiations, Welsh Conservative leader Andrew RT Davies has said.
Mr Davies said the first minister could not handle the "biggest constitutional challenge of our time" alone.
He said the Welsh Government should be reconfigured to give "strong and constructive representation" to UK ministers on EU negotiations.
The Welsh Government said Carwyn Jones was "best placed to lead on Brexit".
Mr Davies pointed to an assembly committee report criticising the Welsh Government for a lack of contact with Irish ministers to discuss the likely impact of Brexit on ports.
"More than 400 days after Wales voted to leave the EU, Wales remains without a Brexit ministry, unlike its counterparts in Scotland and Westminster," he said.
"In order to ensure that Wales' national interests stay at the centre of Brexit negotiations, we need a department led by an experienced minister solely dedicated to this process.
"It's a job too big for one man alone and there's a real danger that in trying to juggle domestic issues with the biggest constitutional challenge of our time, the first minister will allow one or both of these responsibilities to flounder.
"A Welsh minister for Brexit could deliver strong and constructive representation to the UK government and facilitate better working with the devolved nations - not barrack idly from the sidelines as the first minister has so far contented himself to do."
A Welsh Government spokesman said Mr Jones had been "fighting vigorously for Wales' interests ever since the referendum result was known".
He said the first minister had met and discussed Brexit issues with Prime Minister Theresa May, Brexit minister David Davis, the EU's negotiator Michel Barnier and his counterparts in Scotland and Northern Ireland, among others.
Mr Jones was "ably supported" by Finance Secretary Mark Drakeford, he added, who represents the Welsh Government in the Joint Ministerial Committee (JMC) on Europe, and by a European transition team of civil servants.
He claimed the "main barrier" to effective joint working was the "unwillingness" of the UK government to call any meetings of the JMC since February or "consult properly with us on key issues".
The spokesman urged Mr Davies to stop "barracking at the Welsh Government from the sidelines" and put pressure on his Conservative colleagues in Westminster to "live up to their undertaking to agree their approach to the Brexit negotiations with the devolved administrations".