Ronaldo took his tally to 109 goals in 178 senior caps by scoring twice from the penalty spot in Portugal's 2-2 draw with France in Budapest on Wednesday night which ensured they qualified from Group F as one of the four best third-placed teams at the tournament.
The Juventus forward, 36, is currently the top scorer at the Euros with five goals, and could surpass Daei's record when Portugal face Belgium in the last-16 in Seville on Sunday night.
After his record was equalled, former Bayern Munich and Iran star Daei wrote on Instagram: "Congratulations to Cristiano who is now one goal away from breaking the men’s international goal scoring record.
“I am honoured that this remarkable achievement will belong to Ronaldo – great champion of football and caring humanist who inspires and impacts lives throughout the world. Vamos!”
Euro 2016 winners Portugal came from behind to take a point against France and ensure they secured safe passage into the last-16. Opponents Belgium will have 48 hours more to prepare for their upcoming tie, though the holders will not make any excuses.
"It is not a disadvantage," said manager Fernando Santos. "Rest is very important, we have to recover so that they are fresh. We cannot use this as a handicap.
“Let's see if there have been any changes in Belgium, let's analyse the team and prepare for the game with the usual goal: to move forwards."