A Fine Gael TD for Dublin Mid West has called on An Post to change the name of its Passport Express service for customers.
Emer Higgins described it as outdated and misleading and said the service was introduced before it became possible to renew the documents online.
Speaking on RTÉ's Today with Claire Byrne, Ms Higgins said people would be much better off renewing their passports online as it is a cheaper and quicker service.
She said she has raised the issue with Minister for Foreign Affairs Simon Coveney, who, she said, has told her he will speak to An Post about it.
"I get contacted regularly by people who have concerns about passport applications. And it's particularly frustrating for people to find out that they have inadvertently opted for the slowest possible way of getting a passport," she said.
Ms Higgins said there are record breaking volumes of passport applications currently and half a million more applications are expected this year.
She said the passport office has already processed 80% of the total number of applications that were issued last year, which was also a record breaking year.
"I think it's about 5,000 are being processed every single day. And just in terms of this year, the last four months, we've processed 80% of the total number of passports printed last year, and last year was a record year," she said.
She also said that more staff are needed and welcomed the fact that new staff started last week.
"There has been a doubling of people in the passport office in the space of a year and that's a significant investment and what we need."
Ms Higgins said that passport renewals can be really stressful for families and said more investment must now be made in technology so photographs that do not meet criteria are caught in earlier stages.
In addition, she said, many of her constituents are reporting problems with the garda signature, which can be as simple as a date on an application that does not correspond with a station logbook.
There is no reason why this problem cannot be solved online, she said, instead of relying on people to make phone calls to garda stations.
'People want real time information'
Meanwhile, Sinn Féin's spokesperson on Foreign Affairs and Defence called for more resources to be put into the passport office, as well as the installation of an Irish passport office in Northern Ireland.
Wicklow TD John Brady said 400 Irish citizens are applying for an Irish passport every day and said he heard of one person trying to call the passport office 378 times in an attempt to speak to a "human being".
He also claimed that the online webchat is "absolutely impossible".
Describing communication as key, he said that people want "real time information" about when they can expect to get their passport and what the problems with their application are.
He said that for children's and first time passports, the Passport Express service is causing a difficulty, which despite "being sold" as a swift three months express turn around, in a lot of cases this date is being exceeded by four to six weeks.
Mr Brady said he did not think the issue was An Post, rather with outdated mechanisms such as the Passport Office processing paper applications and having to make phone calls to people to verify details.
"People are being given a target date and are not told until two or three days before the target date that additional information is required.
"A lot of people have booked their holiday based on the target date and when additional documents are needed, it will then add at least two or three weeks to delivery time," he said.
Mr Brady said that one of the fallouts from Brexit is that a lot of people in Northern Ireland are applying for Irish passports, which is adding "huge additional burdens" and called on a passport office to be opened in Northern Ireland.