Ulster Bank told investors in London that it saw a lot of evidence of "strategic defaulting". This is where people can meet their mortgage payments but choose to use the money for something else.
Mr Brown and fellow executive Stephen Bell said the bank would go to the courts to seek repossessions.
Ulster Bank claims that no payments are being made on more than a third of the mortgages it has issued. The average mortgage in arrears has €173,000 owed on it.
Typical repayments of €650 a month are being received by the bank. But if homeowners had to rent a similar property, they would end up having to pay €1,000 a month, Mr Bell said.
The bank said it would meet targets being set by the Central Bank for resolving problem mortgages "mainly via legal routes".
All banks have to offer a long-term solution, which includes repossession, to half of those in arrears by the end of the year.