Eriksson accuses Ask of having hid behind the police and the prosecutor's office, by referring responsibility to them, when the case broke in 2010, reports the news agency TT. The surveillance is believed to have been administered from the US embassy in Stockholm.
Ask responded that she acted "by the rule book" when reports came in November of that year that the US embassy had a special unit gathering intelligence in Sweden.
Although a formal investigation was launched, the case never ended up in court because the embassy declined to answer the prosecutor's questions, reports TT.
The opposition Green and Left Parties both reported Ask to the Constitutional Committee, saying too many questions in the case, and her attempts to get to the bottom of it, were left unanswered.
Ask does not agree.
"The Justice Ministry has been very clear with how we acted and what information we had access to," Ask told the committee today.
"In that way, we followed the rule book and I don't think there is any reason to criticise me or the government."
Committee chair Peter Eriksson, a Green Party MP, expressed his dissatisfaction at Ask's answers, telling Swedish media she had shied away from her political responsibility.
"Still today we haven't been able to map out what kind of activity was taking place," he says.
"And the government has done far too little to find out if it was legal."