Welsh support for the UK could be in doubt if Theresa May does not listen to concerns about devolution, the first minister has warned.
Carwyn Jones told The Guardian newspaper that people's "sense of disengagement with Brussels" could attach itself to London after Brexit.
The UK government said it will trigger the Article 50 process on March 29.
Mrs May, visiting Swansea, promised to seek the "best possible deal" that would work for everyone across the UK.
Mr Jones told The Guardian the prime minister had a "tin ear" on matters of devolution.
He warned the future of the UK could be under threat if the UK government did not listen to the other administrations.
"If they are not careful, people's sense of disengagement with Brussels will simply attach itself to London," he said.
"They are giving the impression sometimes that they do not listen.
"And what kind of message is that to the people of Wales?"
Amid calls in Scotland for a second referendum on independence, the first minister said Wales needed to see a "dividend" for his government's continued support of a United Kingdom.
"Otherwise people in Wales are going to start saying, well, the government is listening to the Scots, we need to be like them," he said.
"And that's a dangerous path for the UK."
Last week, Scotland's First Minister Nicola Sturgeon announced her intention to seek approval for a second independence referendum, to be held between Autumn 2018 and Spring 2019.
Mr Jones met Mrs May in her visit to Swansea on Monday, during which she also signed the £1.3bn Swansea Bay Region city deal.
Following the meeting, the first minister said the talks had been "constructive".
"It was made clear that Welsh interventions had helped change and strengthen the UK positions on transition arrangements and on workers' rights," Mr Jones said.
He called for more "partnership working" in the vein of the city deal as Article 50 approaches.
Mrs May said she wanted to get "the best possible deal for the United Kingdom that works for everyone across the United Kingdom".
She said the objectives included a "good free trade deal" and co-operation on matters such as security.
Later in the afternoon, Mr Jones warned the assembly's constitutional and legislative affairs committee there could be Supreme Court challenges if the UK government took back powers from Europe and then decided which were to be devolved.
"I think that's wrong," he said. "That's not the way we read our devolution settlement. It is the way that many in the UK government see it."
He also told the committee, meeting in Newport, that it was "not always clear" that the Wales Office had "much influence" within the UK government.