The Minister for Health, Social Services and Equality Ana Mato announced the change of heart in response to a question from Lourdes Ciuró, an MP for Catalan's CiU separatist party.
Ciuro proposed a private members bill in August demanding to know why a planned extension to paternity leave had been indefinitely postponed.
Mato answered by saying that adding two extra weeks of paid paternity leave would cost the state €245 million ($307 million) per year.
"The government has made the utmost effort over the last three years to overcome the terrible economic situation that we find ourselves in. That is is reason why we haven't been able to implement this measure, which would have a significant impact on the Social Security budget, which could not cope with it at this time," said Mato.
She added: "Right now we can't extend paid paternity leave from two weeks to four. When it is possible, this government will do it."
Spanish daily La Voz de Galicia reported that Ciuró responded to Mato's statements by saying, "Managing affluence is easy. Now that skill is required, it's not good enough to just tell me that there's no money."
Ciuró said that unclaimed paternity and maternity benefits from 2013 would cover the cost and noted that the cost of increasing the extension would represent only 0.057 per cent of the social security budget.
At present, men in Spain are entitled to a maximum of 15 days fully-paid paternity leave (paid by the state) in the case of birth, adoption or fostering, enough to put the country 8th in the EU paternity rankings.
Sweden leads the way with 480 days (16 months) shared between mothers and fathers, the first 390 days of which are remunerated at 80 percent of total salary. At least 2 months must be taken by each parent.
Germany introduced a new system in July this year which added reduced-hours work flexibility to the already-generous allowance of a combined 14 months of paid parental leave, with neither parent taking less than two months or more than 12 months.
In Austria, both parents are entitled to parental leave until the child reaches the age of 24 months provided that the parent taking leave lives in the same household as the child. Parents doing so receive an allowance.
Denmark's system is complicated, with new fathers receiving six weeks leave at slightly less than full pay, with the cost split between the employer, the state and private employment unions.
But there are countries with even less paternity leave than Spain: Switzerland (3 days), Lithuania and Belgium (10 days), Slovenia (11 days) and Cyprus (no days).