The electronic communications regulator, Comreg, received 3,477 complaints from Eir customers in the first nine months of the year.
This amounts to two thirds of the overall number of complaints the regulator received during that period.
Speaking at the Oireachtas Transport and Communications Network Committee, Comreg chairperson Garrett Blaney said Eir customers were subjected to "unacceptable waiting times over an extended period during the last couple of months".
He appealed for further powers to impose large financial penalties without having to go through the courts.
Chair of the Committee Kieran O'Donnell asked Comreg to write to the committee detailing the specific legislation that they require.
He said that it is clear that Comreg are "toothless" when it comes to non-compliance.
However, Mr Godfrey said that it was not possible for the regulator to take Eir to court.
He said that long waiting times are not in themselves a breach of the obligations that providers must adhere to.
However, he said that some of the problems underlying those calls might be a breach that Comreg can pursue.
Mr Godfrey said that Comreg cannot tell an operator that they must answer phones within a certain time, but they can say that operators need to have an effective way for customers to log complaints.
"If they fall down on that part of the process then we can take sanctions," he said.
She told members that remote working, a reduction in staff numbers, and IT challenges led to disruptions in Eir's customer service operations.
During the pandemic, some customers complained of having to wait for periods of more than an hour to speak to customer service staff.