The Spanish capital was unsuccessful in its attempt to host the 2012 and 2016 games, but that could now play to its advantage with 28 of the its proposed 35 venues already constructed.
And Rajoy was also keen to stress the country's experience in hosting big sporting events and large numbers of visitors.
"Madrid has a great advantage," he told a press conference on Monday.
"Of the sports facilities needed to hold an Olympic Games, 80 percent are already built. In addition, it is a city well used to hosting major events.
"Spain is a country too that is fortunately very used to welcoming visitors. It is the third leading country in the world for annual number of visitors, with 58 million tourists coming to our country last year alone."
Rajoy also played down the concerns that hosting the Olympics is the last thing that Spain's beleaguered economy needs in the midst of a crisis.
He claimed that the bid had public support and that money would not have been spent on a third bid if they did not believe it could succeed.
"I have stated what I believe is the general feeling of Spanish society. Madrid has already attempted to win the bid on two previous occasions and was not successful then, but now we are convinced it can be so we are going to battle hard to win.
"We are ready and prepared to host an event of the importance of the Olympic Games and we would do so very proudly. We are absolutely convinced that with the backing of people in Spain it would be a huge success for Madrid, Spain and in general for the whole Olympic movement."
The evaluation committee will visit sites across the city for the next three days before filing their report to IOC members.
Tokyo and Istanbul are the other cities in the running for the 2020 Games with a final decision on the host city to be taken in Buenos Aires on September 7th.