Former Iran striker Daei, who scored 109 goals for his country in 149 appearances before retiring as a player in 2007, said on Instagram he was "honoured" Ronaldo had joined him at the top of the list.
Daei said: "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!"
Ronaldo has strengthened his case to be considered the best player of all time.
His double for Portugal against France in Budapest extended his record Euro finals tally to 13 after he became top scorer outright with his two goals against Hungary in their opening group game.
Ronaldo, the leading Champions League goalscorer, also surpassed Miroslav Klose's 19-goal record for most goals combined at the World Cup finals and Euro finals. The Portuguese now has 20.
Daei, who had spells in the Bundesliga during a 20-year playing career, and Ronaldo are the only players to score more than 100 international goals.
The Iranian scored his 109th goal for his country against Costa Rica in March 2006 – the same day Ronaldo netted his 10th and 11th goals for Portugal in a friendly against Saudi Arabia.
Former Arminia Bielefeld, Bayern Munich and Hertha Berlin striker Daei went on to become a successful manager in Iran and had a spell in charge of the national team from 2008-9.