Welsh Secretary Cheryl Gillan says the closure of the passport office in Newport is not inevitable.
She said no decision had yet been taken and that she was lobbying ministerial colleagues and meeting the head of the passport service next week.
First Minister Carwyn Jones is to write to the prime minister, claiming the UK government has "lost the plot".
The Public and Commercial Services Union (PCS) said the closure, with 300 job losses, would be "devastating".
Ms Gillan has condemned the union for the "irresponsible" way she said it revealed details on Friday of the threatened closure, but said she could not rule out job losses at the office.
Speaking on the Politics Show Wales, she said: "The Identity and Passport [Service] is looking at their operations right across the board and I understand they will be starting a period of formal consultation about the Newport office on 19 October.
"No decisions have been taken yet and that is why I've invited the chief executive to a meeting in my office next week.
"I was already talking to ministers when this news came out sadly on a Friday afternoon - I don't think that is really a very good time for people and families to learn about the proposed talks.
"I'm not going to say there are not going to be cuts to jobs in Wales, because that has been acknowledged right across the board."
Ms Gillan dismissed claims that Wales would suffer disproportionately from any coalition government cuts.
She said: "Wales is not being singled out and I will fight for every single job in Wales, whether it's in the public sector or the private sector."
The passport office at Newport opened in 1967. It is one of seven regional passport offices in the UK but the only one believed to be closing.
The Labour Party in Wales has called the doubt over the office's future a "dangerous precedent for things to come" for the more than 30,000 civil servants in Wales.
Carwyn Jones has said the announcement had come "completely out of the blue" and that "the way that this has been handled, frankly, is unbelievable".
He said there was no economic argument to close the Wales passport office which also serves people in the west of England.
The Identity and Passport Service said its system currently had too much capacity which could only be resolved by closing a regional passport centre.
It said analysis had found that closing Newport would result in the greatest reduction of spare capacity at the lowest cost to the taxpayer.