The move by the Department for Work and Pensions (DWP), reported in newspapers on Wednesday, will seriously deplete services in some of the most deprived areas of the city, Mr Roberston said.
Raising the issue in the Commons during PMQs, he demanded to know why the Government is slashing services by 50% in Glasgow compared to 20% nationally.
He said: “Some of the most deprived communities in the country are in Glasgow, and today we learnt, apparently, that the Government plans to close job centres in those very communities - in Parkhead, in Bridgeton, in Easterhouse, in Castlemilk, in Langside, in Anniesland, in Cambuslang and Maryhill.
“Is it true that the Government is planning to close these important offices and add misery to the many tens of thousands of people in Glasgow who currently use these centres?”
Leader of the House of Commons David Lidington, who was standing in for Theresa May who has been visiting Bahrain, said all departments must look at the number of offices they have and he would get the Work and Pensions Secretary Damian Green to write to him with details of the closures.
But Mr Robertson said “that’s not good enough”.
He added: “The Leader of the House is correct to say that the Department for Work and Pensions has plans to cut the estate by 20%.
“What the DWP is planning to do to Glasgow is to cut it by 50%. Why is this Government planning to disproportionately cut vital job centres in some of the most deprived communities in our country? Why?”
Mr Lidington said: “The key element in any such decision that a Government department has to make is not the raw number of offices that there should be, but about how accessible the offices and the services which they provide continue to be to the people who need to use them.
“And I am absolutely confident that it is that criteria that is at the heart of my right honourable friend’s thinking in planning for the future of offices in Scotland and everywhere else in the United Kingdom.”