The interim certification system that allows vaccinated people in Northern Ireland to travel abroad is under "extreme pressure", the Department of Health (DoH) has said.
Some people applying for a certificate have had trouble obtaining one online, via post and by telephone.
The department's statement came before it launched its vaccine certification app, CovidCertNI, on Friday night.
It allows people to show they have had two doses of a Covid vaccine.
Proof of vaccination is required to enter some countries.
The app can now be downloaded from the Apple App Store and is expected to be available through the Google Play store at some point this weekend.
The Department of Health said that people travelling between 26 July and 31 July can apply for a certificate either using the app or the interim system.
'Never been so stressed'
However the department has asked that only those who are travelling up to the end of July download the app, warning that it "is likely to be popular and this might cause delays or capacity problems".
Health Minister Robin Swann said there had been "monumental efforts" made by his department in releasing the app.
The interim scheme remains in place until the app has been fully rolled out - the department said it is aware some users are facing difficulties and asked for people to "be patient" as it addresses the issues.
However, some users have reported technical issues and delays around submitting information into the system.
In order to access the certificate, a verification webpage requires users to submit a photo of themselves along with a photo of their passport's information page.
Those waiting for the certificate risk having to abandon travel plans altogether, potentially losing money.
One man told BBC Radio Ulster's Talkback programme that he had been trying to get a digital vaccine certificate for nearly a week and that the delay could see him and his partner lose the money they paid for a holiday to Malta.
Dan told the programme he had "never been so stressed".
After applying for a certificate, he said he received an email from the Health and Safety Executive telling him it was available for download.
"My certificate is sitting online somewhere but I can't access it because of NI Direct's account verification system," he said.
Each time Dan tried to submit the photo of his passport it was rejected by the webpage, which told him it "could not see the corners of the document".
"It's not very surprising - a passport has round corners," he said.
An alternative way to apply for the certificate is by sending copies of vaccination and passport documents to be approved manually.
It is supposed to take no longer than 48 hours.
But Dan was still waiting three days later.
'Avoid blocking the helpline'
There is a helpline for the public to call if they are having difficulty obtaining a certificate.
The Department of Health have asked people not travelling within the next few days to "avoid blocking the helpline for those with more pressing needs".
Dan said he has tried the number multiple times without success.
"I don't know whether to scream or cry at this stage," he said.
"There's no means of talking to a human being about it - that from a government agency is ridiculous."
Dan is not the only one struggling with the application system - Claire Greenlee told BBC News NI she has been trying to obtain a certificate for days with no success.
She described the vaccine certificate scheme as a "shambles".
"The website is so temperamental," she said, complaining of error messages and being unable to access the certificate.
"I eventually get through to the helpline, only to be told there is nothing they can do - they are only an information service.
"I'm due to travel on Sunday but at this rate I will be going nowhere," she added.
Details of how to apply for the interim scheme are available on the NI Direct website.