Mr Pena Nieto said it had damaged people's faith in the presidency.
He said he had not broken the law and promised to redouble efforts to fight corruption.
Mr Pena Nieto's party, the PRI, suffered severe losses in recent local elections.
He was addressing political leaders at the unveiling of a new anti-corruption system that increases the monitoring of politicians.
Mr Pena Nieto is facing presidential elections in 2018.
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In an unusually frank apology, he said the scandal had damaged the Mexican people's faith in the presidency and the government.
"For this reason, with all humility I ask your forgiveness."
"I repeat my sincere and profound apology for the offence and indignation I have caused you."
Mr Pena Nieto had reacted angrily at the time when he and his wife were criticised for buying the luxury home from Grupo Higa, a major government contractor.
His wife, Angelica Rivera, denied wrongdoing and said she had bought the house with earnings from her career as an actress.
She later returned the mansion, which she had been paying for in instalments.
It emerged later that Mr Pena Nieto's finance minister had also bought a house from the same contractor.
A government investigation later found no evidence of wrongdoing.
Correspondents say the scandal may have also damaged Mexico's relations with China because they cancelled a a multi-billion-dollar contract won by the sole bidder, a Chinese-led consortium to build a high-speed rail link.
Grupo Higa was part of the consortium.
Mexican President Enrique Pena Nieto has apologised for a scandal involving his wife's purchase two years ago of a $7m house from a government contractor.