Mr Barclay asked Royal College of Nursing general secretary Pat Cullen to formally notify employers of strike plans “without delay” so they can prepare for the walk-out. Nurses are expected to strike on December 15 and 20 unless they win a 19 percent pay rise.
Ms Cullen said she would only agree to talks if the Government negotiates a new pay deal.
Mr Barclay urged her to “reconsider”, saying he was “disappointed you’ve taken this unprecedented step”.
He wrote to the RCN urging its representatives to “come back to the table” for talks, and a Whitehall source suggested these could include subjects such as pension arrangements, holidays, rosters and the availability of free coffee.
In her response to Mr Barclay, Ms Cullen said: “If the negotiation table is empty, we can see you are not serious about progress.”
The nurses’ stand-off comes as Britain faces a further wave of strikes. Workers who clean trains have voted to strike, seeking a wage rate of £15 an hour.
Rail, Maritime and Transport union general secretary Mick Lynch said: “We will fight to end the super-exploitation of contracted-out cleaners and will not rest until these greedy companies pay up.”
The RMT has called a series of walkouts in the coming weeks.
Royal Mail workers have more strikes planned before Christmas, Border Force staff are due to leave their posts in the coming weeks, and schools in Scotland closed last week after teachers staged industrial action.
Former Conservative leader Sir Iain Duncan Smith has called for a loophole to be closed to stop strikers receiving tax-free payments from trade union war chests.
It is reported at least 22 unions have political or strike funds of more than £100million.
Sir Iain said: “All earnings should be taxed. If the union is paying them, then the workers should pay tax on it.”
Sir Bernard Ingham, Margaret Thatcher’s former press secretary, claims the strikes are a political weapon to oust the Conservatives from power.
He said the RMT wants to “bring the Government down in order to secure a Labour government which would do their bidding”.
He had clear advice for ministers, saying: “Concede not a penny. Secondly, warn them that if these strikes continue then you will legislate to ban strikes in public services.”
Sir Bernard warned that nurses risk a PR disaster. He said: “Can you imagine anybody doing worse damage to their reputations than nurses going on strike?”
Robert Colville, of the Centre for Policy Studies, said: “The right to strike is fundamental but so is the need to keep essential public services going during industrial disputes.
“If not, it is the most vulnerable who suffer.”
An RMT spokesman said it is “complete nonsense” that the union is trying to bring down the Government.
He added: “The union is wholly focused on getting a negotiated settlement on job security, working conditions and pay for its members in the national rail dispute.
“Only the electorate through the ballot box can change the Government.
“A threat to democracy is the minimum services bill which would make effective strike action illegal.”