RTÉ has requested a breakdown in Eurovision voting numbers from the European Broadcast Union (EBU) and its voting partner Once.
It comes after Spain's public broadcaster, Radio Televisión Española (RTVE), called for a "complete review" of the voting system to "avoid external interference and manipulation", referencing votes received by Israel in the public vote.
RTVE President José Pablo López said he had "expressed great concern about Israel's participation, transparency, legitimacy and perceived integrity of the current voting system".
Flemish public broadcaster VRT also said it was "demanding full transparency" from the EBU in relation to the televoting during Saturday's final.
Televoters in both Spain and Belgium awarded Israel 12 points, while their juries gave the country zero points.
Ireland, meanwhile, awarded Israel 10 points in the televote and seven points from the Irish jury.
Overall, the Israeli entry, Yuval Raphael, finished second in the contest with her song New Day Will Rise.
Austria's entry JJ took home the trophy with 436 points, ahead of Israel on 357 points.
Israel attained the highest score from the public vote.
In a statement, Director of the Eurovision Song Contest Martin Green, said it took the concerns raised by the broadcasters "seriously" and that the EBU had contacted several broadcasters since the final regarding voting in the competition.
He said: "Now the event has concluded we will have a broad discussion with participating broadcasters, to reflect and obtain feedback on all aspects of this year's event as part of our planning process for the 70th Eurovision Song Contest next year.
"It is important to emphasise that the voting operation for the Eurovision Song Contest is the most advanced in the world and each country’s result is checked and verified by a huge team of people to exclude any suspicious or irregular voting patterns.
"An independent compliance monitor reviews both jury and public vote data to ensure we have a valid result."
A spokesperson for RTÉ said the broadcaster was looking forward to participating in the discussions and review outlined by Mr Green.
