David Cameron on a visit to Newtown, Powys earlier this month
Prime Minister David Cameron is expected to visit the Welsh assembly on Monday, less than a week after his coalition government took office.
The Conservative leader promised to visit Wales within days when he spoke to Labour First Minister Carwyn Jones last Wednesday.
Welsh Secretary Cheryl Gillan said she would not "dicate" to the assembly government when to implement cuts.
Mrs Gillan said it was the "fair route" to allow ministers in Wales to decide.
Mr Cameron's visit to Wales follows a similar one to Scotland.
He travelled to Edinburgh last Friday and held talks with Scotland's First Minister Alex Salmond.
The prime minister has already confirmed his commitment to devolution and his enthusiasm "to work productively" with the assembly, which is governed by a coalition between Labour and Plaid Cymru.
In Scotland, Mr Cameron called for an "agenda of respect" between the Westminster and Holyrood parliaments.
First Minister Carwyn Jones has said he wants the assembly government to have a "constructive relationship" with the new Conservative-Liberal Democrat UK government.
As soon as the coalition government was formed at Westminster, Mr Jones said his main aim was that "the priorities of the people of Wales come first".
Mr Jones sent his congratulations to Mr Cameron and said he looked forward to a "businesslike relationship with the new UK government".
Cheryl Gillan, who is Welsh secretary in the UK government, has said the economy and a referendum on more legislative powers for Wales were her first priorities in the role.
Speaking on BBC Radio Wales, Mrs Gillan said the new administration would be letting the assembly government decide how it would be contributing to the cuts to be made across the UK.
She said they had "no intention of dictating to the Welsh assembly government, quite the reverse".
"We respect the institution and we acknowledge they have already set their budget for Wales and I think that's the fair route to take and I am sure that will be confirmed later today.
"I'm not going to micro-manage the budget responsibilities of the Welsh Assembly Government."
On the question of Wales' funding, she commented: "I fully understand the Barnett formula has come under question.
"We have talked about moving towards a needs-based assessment so that we can look at fair funding right across the board in the United Kingdom."
She claimed there had been no work done on the wording of the question to be asked in any referendum on further powers for Wales, which she indicated could lengthen the time needed before one could take place.
It had previously been suggested a referendum could happen in the autumn.
"I'm determined that we will press ahead .. and we are going to move forward as rapidly we possibly can on the referendum process," said Mrs Gillan.
"Can I just get this caveat in though? Nobody would forgive me if I cut corners and went for half measures on this.
"So we have to do a proper job on the referendum to allow the people of Wales to decide for themselves."
Cardiff-born Mrs Gillan, who represents a constituency in Buckinghamshire, said she would remain neutral in any referendum campaign.
Meanwhile, Conservative assembly leader Nick Bourne AM said he "massively welcomed" Chancellor George Osborne's announcement that devolved institutions would be given the option to put off cuts for a year.
"The commitment from the Treasury team gives Wales flexible control over any cuts, as we promised before the election, and is contrary to Plaid Cymru and Labour claims that Wales would be ignored by a Conservative Government," said Mr Bourne.
"It is now in the hands of the assembly government and up to them to indicate whether they will be accepting this offer."
Welsh Liberal Democrat leader Kirsty Williams AM said: "Given our high dependence on the public sector, it would be wise for the Labour-Plaid government to defer cuts to the Welsh budget for a year so that we have time to remodel our economy in a more sustainable and long-term manner".