RTÉ reported a net deficit of €13m in 2018, according to its annual report.
The media organisation said although there had been a modest increase in total revenue, and a reduction in operating costs, the cost of special events - including the Papal Visit, the Presidential Election and coverage of the FIFA World Cup - contributed to the overall deficit.
In 2018, RTÉ had 39 of the top 50 most watched television programmes here and RTÉ.ie recorded almost 62 million monthly average page views.
Director-General Dee Forbes said there was much to be proud of, including in-depth coverage of Brexit, round-the-clock output on Storm Emma, and special programmes, including the Late Late Toy Show, which attracted more than 1.5 million viewers.
However, she said that although the broadcaster was "full of programme ideas", every day it had to curtail its own ambitions and the creative ambitions of the independent production sector due to constrained resources.
She said it would not be possible for RTÉ to maintain and enhance what it does, and fulfil its remit, without action from the Government and a solution to the funding of public service media in Ireland.
Ms Forbes said the case for increased public funding for RTÉ had been made in numerous independent reports over the past five years, including the BAI review in 2018, which recommended an increase of €30m.
The case for reform of the TV licence system had also been made, but she said to date there had been no substantial response from the Government.
Ms Forbes said the organisation was in a review process and everything was being examined.
Speaking to RTÉ News, she said issues contributing to the deficit included the broadcasting of special events such as the Papal Visit and the Presidential Election, as well as a challenging commercial environment, which has been affected by Brexit.
Ms Forbes said RTÉ could do a lot to help itself, but it needed action from Government and that had not come in to play, and that the licence fee system was no longer fit for purpose.
When asked if RTÉ is considering further cuts to staff or output, Ms Forbes said the broadcaster was in a review process and that there will be more to come on that in the autumn.
She said everything was on the table and the situation was serious. RTÉ cannot continue as it is and a lot of work was being done to come up with solutions, she said.
Ms Forbes added that RTÉ cannot continue in deficit because it will not have the cash to facilitate those deficits.