The number of people making disclosures about offshore accounts may top 10,000 with the Revenue Commissioners already collecting €184 million from some of those involved.
Revenue chairman Mr Frank Daly yesterday signalled that this might rise to €1 billion in time, although he said he was "loath to speculate" on a final figure.
At the Oireachtas Public Accounts Committee, Mr Daly said those with an offshore tax liability had until Monday to make a voluntary disclosure or they could face penalties, interest and publication of their names.
He said if a disclosure was made, those with a liability had until late May to make a payment. Up to recently, 3,500 disclosures had been made, but Mr Daly said this had risen to 5,000 this week.
"I am encouraged by the response so far. People are taking this matter very seriously."
He said even with a postal strike those making a disclosure could still fax or drop their forms into their local Revenue office. He said those involved were learning from previous experience.
The whole offshore investigation was set up last year. Several leading banks, including Bank of Ireland and Permanent TSB, wrote to their customers alerting them to a potential liability. Several of these banks have maintained operations offshore.
Mr Daly said last December that he met the chief executives of the main financial institutions with offshore branches or subsidiaries and obtained their co-operation.
Several members of the committee pushed Mr Daly to speculate on what might ultimately be collected from those making disclosures. In response to a question from Mr Paul Connaughton TD, Mr Daly acknowledged it might be up to €1 billion, but then said he did not wish to speculate. He said it was not his policy to "over promise".
Mr Daly said more than €1 billion had been collected following the various revenue investigations of recent years.
He said €49 million came via the NIB/CMI Bonds investigation; about €41 million from the Ansbacher investigation; some €24 million came via evidence produced at various tribunals and €726 million came from the bogus non-resident accounts investigation. The remainder was from the offshore investigation to date.
This investigation was triggered after the Revene approached several leading banks including about offshore operations in the Isle of Man and Jersey. The banks subsequently wrote to their customers.
Anglo Irish Bank and Irish Nationwide also wrote to customers about offshore accounts.
Asked whether banks might be prosecuted for aiding and abetting tax evasion, Mr Daly said tax evasion began with the individual but Revenue would study what the banks' role might have been.