The helpline set up for queries on the Digital Covid Certificate received over 2,000 calls in its first two days according to the Department of Health.
The department also said that more that 2 million certificates that allow travel in the EU have been issued by post and email.
Many people have complained that they could not get through or were left on hold for up to four hours to the new helpline number 1800 807 008.
The department had said the number of staff had been increased to 55 and that there will be 90 by the end of the week.
There were 1,160 calls on the first day of operation yesterday and over 1,000 by lunchtime today according to a department statement.
Staff are prioritising queries from those wishing to travel in the "very near future" relating to Recovery Certs for those who have had Covid and Digital Certs for those who were vaccinated.
Those who have been vaccinated should receive their Certs automatically and the government has asked people to check their email including spam folders.
It said 2 million of the EU Digital Covid Certificates have been sent in the past week.
"A contact centre has been created at exceptional pace to manage the required workflows and communications, while meeting all data protection requirements. This has required an incredible effort across multiple government agencies to put in place the people, processes and technology required," the statement added.
Those who were vaccinated privately are being asked to contact their provider.
It says that many people who are contacting the helpline are not due to travel soon and the department points out that these Certs can be applied for at any time over coming weeks.
The public are being advised that up to date information is available at gov.ie/travel.
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Earlier, callers to the helpline were told to expect to wait at least 90 minutes before they can talk to an agent.
The advice is to wait five days after their final dose for a vaccination certificate and to check their email spam folder.
The voice message says that those travelling within the next seven days are being prioritised.
However, one member of the public due to travel tomorrow said they have waited nearly four hours to talk to an agent.
When they got through they were told the call centre did not have their records and that they would have to ring back and start the process again.
In a statement, the Department of Health asked that only people who are travelling in July should contact the Covid Certificate helpline. It also said an increased number of agents are available.
A Government spokesperson said the line would be able to take a far higher number of calls and said those ringing will not get the call failed message.
The Department of Health said yesterday that a very high number of calls led to difficulties on the original helpline's first day of operation.
The number 1800 851 504 was provided for queries and for those who had recovered from Covid-19 to apply for the cert.
Many callers had complained however that they could not get through to the number yesterday.
The Department of Health said it was working to increase capacity on the helpline, but blamed a "very high number of calls" for the difficulty.
Those who have been fully vaccinated are supposed to receive their certs automatically.
Additional reporting: Mícheál Lehane