The Minister for Justice, Mr McDowell, has said he is concerned at security within An Post following a huge robbery in Dublin last week.
Three staff members were tied up and around €250,000 was stolen in a robbery at the post office in Rathmines last Monday.
Mr McDowell said he would be raising the way An Post stores large cash reserves with the Minister for Communications, Mr Dempsey. He said he would be asking Mr Dempsey if An Post had "adequate" security arrangements in position.
"If it is the case that on some occasions they store up to €3 million in safes, what precautions are they taking?" he said.
"This kind of money does enormous damage when it falls into the hands of criminals and criminals are willing to do dreadful things, including killing people."
A spokeswoman for An Post said they would not comment on security issues.
The Labour Party justice spokesman, Mr Joe Costello, described the criticism of An Post as "unwarranted" and "very strange".
He said is was Mr McDowell's responsibility, as Minister for Justice, "to ensure that Garda resources and personnel are allocated appropriately to help intercept and discourage robberies from any financial institution".