Arrangements were being finalised yesterday to pay out millions of euro owned by Gama Construction employees and held in accounts in a Netherlands bank.
The firm's Turkish staff claim they were never told about the accounts in Finansbank, in Amsterdam, into which a portion of their wages was paid.
Gama, which yesterday again denied allegations of migrant worker exploitation, insists that employees have had access to the accounts at all times.
The bank has now moved to assure Minister for Enterprise Micheál Martin and Siptu, the union representing most Gama staff, that money in the accounts will be paid out immediately.
Mr Martin said yesterday the bank had told him it had already received instructions from Gama on behalf of 660 employees about accessing their accounts.
"The bank has said that 281 of these instructions have been complied with and they estimate that the remainder will be completed by the close of business this [Wednesday] evening.
"Finansbank has agreed to put in place a process with the Department of Enterprise, Trade and Employment to allow the remaining workers to access their accounts," he said.
Socialist Party TD Joe Higgins, who made public the existence of the accounts, has estimated they hold at least €30 million belonging to current and former Gama employees.
Siptu construction branch secretary Eric Fleming said the bank had written to the union this week assuring it that workers would be given full access to their money. The process of transferring it into the workers' accounts in Turkey had already begun, he said.
Mr Fleming said this was only part of the solution to the workers' concerns, however, as money paid into Finansbank did not cover all the hours worked by Gama's employees.
The firm was now co-operating with the union in the painstaking process of identifying how many hours each employee had worked in overtime and how much they were owed.
"The company has admitted that its own records may not be 100 per cent accurate and is prepared to sit down with us and go through all the details," he said.
Gama has been the subject of an investigation by labour inspectors at the Department of Enterprise, Trade and Employment since Mr Higgins made allegations in the Dáil in February about its employment practices.
In a strongly worded statement yesterday, Gama again denied Mr Higgins's claim that its employees were paid €2-€3 an hour and worked excessive hours. It said its minimum hourly payment for workers was €12.96, in compliance with the agreed construction industry rate.
The claim that workers had been unable to access their accounts in Finansbank was not true. The funds had been "fully and irrevocably available" to each employee at any time, it said.