Senator Eric Abetz has stuck by claims he and Prime Minster Tony Abbott made last year that the Coalition's decision to abolish certain guidelines would not reduce the wages of cleaners.

The opposition's leader in the senate, Penny Wong, called for Senator Abetz's response in the senate to be investigated because he appeared to be misleading the upper house.

Senator Abetz's comments on Tuesday came despite cleaners at the Department of Immigration and Border Protection receiving a $2 an hour pay cut because the protections in the guidelines have been removed.

"When the guidelines were removed in July nobody's pay was cut, nor was anybody's pay cut in August or September or in October," Senator Abetz said.

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Senator Abetz said the cut at Immigration had happened because of a new contract being introduced at that workplace, but his answer did not acknowledge the effects of removing the guidelines.

"I understand any worker who has had their pay reduced would find that very difficult," he said.

His explanation also seemed at odds with his sweeping statement to the senate a year ago in which he said: "no cleaner will have their wages reduced as a result of the guidelines ceasing to apply".

On the same day in June 2014, Mr Abbott said in question time:  "I want to make it absolutely crystal clear that no cleaner's pay is reduced".

During the same response Mr Abbott also said no one could be paid below the award wage, despite protests from opposition leader Bill Shorten that he had not asked about the award wage.

Senator Abetz told the senate on Tuesday wages should be set by enterprise bargaining or the Fair Work Commission and not by government interference.

The annual wages of cleaners who work at the Immigration Department's buildings in Canberra will this year be reduced by thousands of dollars, according to pay slips obtained by Fairfax Media.

A letter sent by the department's cleaners to Immigration and Border Protection Minister Peter Dutton said the pay cut "may not seem like much to you but when you don't earn a lot this really does make a big difference".

"Due to the uncertainty around the removal of the guidelines, the tender of the contractor we work for was based on three different pay rates, " the letter said.

"Unfortunately the department chose to accept a reduced pay rate which the contractor has now passed on to us."