Carwyn Jones has said there is “some way to go” before the Welsh Government can support the Brexit bill transferring EU law to Parliament.
It follows what the first minister called a “useful” first meeting with Damian Green, Theresa May’s deputy.
Mr Jones has accused the UK government of planning a Brexit “power grab”.
Mr Green said the talks in Cardiff had been a “step in the right direction” with the need to focus next on areas that needed a common UK approach.
Relations between the two administrations have been strained, with the UK government warning Mr Jones not to “undermine Brexit talks” as he has accused them of trying to take power back from Cardiff Bay.
There have also been concerns that a joint ministerial committee (JMC) – for the Scottish, Welsh, UK and Northern Ireland governments to seek a UK-wide approach to Brexit – has not met in six months.
Monday’s meeting, the first time Mr Jones has met the first secretary, was aimed at addressing concerns about the repeal bill – also known as the European Union (Withdrawal Bill) – which will be debated by MPs on Thursday.
It aims to ensure the rules currently set by European law still apply in the UK after Brexit, while giving the UK Parliament power to change them.
Mr Green was accompanied by Welsh Secretary Alun Cairns, while Mr Jones was joined by the Welsh Government’s Finance Secretary Mark Drakeford.
Mr Jones and Scotland’s First Minister Nicola Sturgeon have threatened to block the repeal bill, saying it does not return powers to devolved administrations as promised – rather returning them “solely to the UK government and parliament” – and imposes new restrictions on Scotland and Wales.
Following the meeting, the first minister tweeted that he had had a “useful first meeting” with Damian Green, but added there was “some way to go” before his government could support the repeal bill.
A spokeswoman for Mr Jones said the Welsh Government had offered and re-iterated a “common sense approach to resolving the current impasse”.
She said the meeting was “constructive” but reiterated that changes were needed to the Brexit bill “in order to protect the rights of the people of Wales”.
“Whilst there was agreement on a number of objectives today, we still need to see a shift in attitude in Westminster about what the devolution settlement means in principle and in practice,” she added.
Mr Green said: “The talks today were conducted in a constructive spirit and were a step in the right direction.
“We both agree that it is vitally important to protect the internal UK market and to avoid making things more difficult and expensive for Welsh companies doing business across the UK.
“To achieve this we will need to adopt a UK-wide approach on certain issues.
“The next step is to discuss those areas that need a common UK approach for the good of businesses and consumers in Wales and across the United Kingdom.
“It is critical that work starts now.”
Mr Cairns added: “More powers will certainly come to Wales as part of this process and that will be an important incentive in pushing us towards an agreement.
“There is a significant job of work to be done and we must keep focus on the outcomes we want to achieve.
“We will keep talking and I am confident we can reach an agreement that works for all parts of the UK.”
Plaid Cymru’s Brexit spokesman at Westminster, Hywel Williams, said talks between the governments would be “futile” unless Carwyn Jones took a “bolder stance” on membership of the single market and customs union.
He asked: “What is the point of the Labour First Minister attending these meetings unless he and his party show real commitment to protecting Welsh jobs and businesses?
“A transitional policy such as that announced by Labour last week isn’t a policy worth having.
“The First Minister must get behind permanent single market membership or risk handing the Tories a blank cheque for a hard Brexit.”