Wales' First Minister Carwyn Jones says he wants a "constructive relationship" with the new Conservative-Liberal Democrat UK government.
Mr Jones said his main aim, with the confirmation of David Cameron as prime minister, was that "the priorities of the people of Wales come first".
The leader of the Welsh Assembly Government said he wanted an early meeting with the new premier.
Plaid Cymru accused Labour of "handing government of the UK" to the Tories.
The Conservative leader in the assembly, Nick Bourne said he was "delighted" by the coalition outcome.
Mr Cameron's arrival in Downing Street means that the two parties in coalition in the assembly government - Labour and Plaid - will have to work with a UK government run by two different parties.
Mr Jones has sent his congratulations to Mr Cameron and said he looked forward to a "businesslike relationship with the new UK government".
In a statement, he said: "It is my intention to have a constructive working relationship with the new Tory/Lib Dem government.
"As first minister, it is my job to lead Wales and make the case for Wales - irrespective of who resides in No 10 Downing Street - and that is what I will continue to do.
"As a consequence, I will be seeking an early meeting with the new prime minister to seek his assurances on such issues."
Mr Jones, who took over as first minister last December, himself heads a coalition Labour-Plaid Cymru government in the Welsh assembly.
Peter Hain has lost his post of Welsh secretary and there is yet no indication who will replace him in Mr Cameron's cabinet. However, Cheryl Gillan has been the Conservative shadow Welsh secretary.
This is a significant and worrying moment for us in Wales
Elfyn Llwyd, Plaid Cymru
Mr Hain had advocated a Labour-Lib Dem coalition with the support of minor parties before that prospect collapsed.
Mr Hain said that while Lib Dems were "fully entitled to link up with the Tories, I am sorry that they rejected the opportunity for a progressive coalition government to fundamentally change British politics".
He said: "We will be taking our role as the opposition very seriously, and holding the Conservatives and Lib Dems to account if they fail to deliver what the country needs and working with them where there is common ground."
Plaid had hoped to play a role in a hung parliament, but that disappeared with the formation of the Tory-Lib Dem deal.
Elfyn Llwyd, Plaid's Westminster leader, claimed that "London Labour had collapsed under pressure" and said a Tory government would "do its worst" to the Welsh economy.
"The Conservative Party has outlined its plans which will have disastrous effects on the Welsh economy - including further 'in year' cuts in addition to those already proposed," he said.
"We haven't heard anything from their new political allies, the Lib Dems, to suggest that protecting jobs and public services in Wales from disproportionate cuts is a red line during their talks with the Tories.
Speaking from College Green outside parliament, new Conservative MP for Cardiff North Jonathan Evans said: "I think that great maturity has been shown by David Cameron and our team in negotiating this deal in moving forward.
"I've been very much encouraged by the way in which the Liberals have taken on board very many of the things that we have been saying during the course of the general election campaign.
His Tory colleague Mr Bourne added: "This agreement will bring stability to government and I look forward to working with the new Westminster team which I am sure will be sensitive to the needs and aspirations of Wales.
"We all want to develop a positive working relationship between the UK and assembly governments, and between Westminster and the assembly to deliver the best possible outcomes for Wales."
The Welsh Lib Dem leader, Kirsty Williams echoed her support for the new governing coalition at Westminister: "This is a historic moment for the Liberal Democrats and I am very proud that we as a party will be able to implement our policies in government.
"Not only are we forming a new government, we are forming a new kind of government - a government based on consensus and of cooperation."
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