The International Olympic Committee IOC.L dropped Doha and Azerbaijan capital Baku at a meeting in Quebec City on Wednesday, leaving Tokyo, Istanbul and Madrid to fight it out for the hosting rights.
The IOC will make their decision on the winning city in Buenos Aires in September 2013.
"Madrid is committed to the Games as a factor for economic regeneration," the president of the Spanish Olympic Committee Alejandro Blanco was quoted as saying in Spanish media on Thursday.
Madrid, who failed in their bids for the 2012 and 2016 Summer Games, were praised in the IOC report for their "clear vision", high levels of government and public support, and the fact that many of the installations required were already in place.
There was a warning, however, as the IOC pointed out "careful attention would need to be paid to Spain's economic outlook".
The Spanish economy is in recession with rising debt costs, the highest unemployment rate in the European Union, and their government is having to impose painful austerity measures to try and reassure investors of its fiscal health.
"There are some weak points we need to improve on," Blanco added, as he stressed their Olympic bid was an "investment" for the country overall.
"Now starts the second half, which will be decisive. Third time lucky."
The mayor of Madrid, Ana Botella, took a similar line in trying to make the economic angle a strength rather than a weakness.
"Now I am convinced that this time we are going to have a winning project," she told local media.
"I think now, more than ever, that the organisation of the Games is a strategic project for the country that will attract investment and unite everyone."
(Reporting by Mark Elkington, editing by Patrick Johnston)
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