The money-for-influence scandals have spread to include his elder brother Lee Sang-deuk, who is also a political mentor and who was arrested July 11, the Yonhap news agency reported.
Lee Sang-deuk was arrested on suspicion of receiving more than $500,000 from two troubled savings banks.
The apology, which included a deep bow behind the podium, was the sixth public apology during Lee Myung-bak single five-year term, Yonhap said.
"Fellow Koreans, disgraceful incidents have recently happened to my family and surroundings and caused so much anxiety to people," Lee said.
"I bow my head and extend my apology for causing anxiety to people due to these incidents."
The apology was made without any mention of his brother or the aides and comes in the final year of his presidency that ends in February.
Formal charges haven't been laid against his brother.
"I had thought that it would be appropriate for me to wait for the results of the investigation by the prosecution but I stand here before you because I judged that it is my minimum duty to pour out my heart to the people ahead of the results," Lee said.
However, former National Assembly Speaker Park Hee-tae and former presidential aide Kim Hyo-jae were indicted in February for their alleged involvement in a political bribery scandal.
Lee said he will "take full responsibility" for the scandals but won't leave office before his term ends, Yonhap reported.
"Situations in and out of the country are so urgent so I can never neglect my duties as president," Lee said.
The elder Lee is a former six-term politician and considered the most powerful figure behind the Lee administration, Yonhap said.
He has been accused of receiving money from Solomon savings bank and Mirae savings bank in return for influencing authorities who were investigating the banks.
Park, the former National Assembly Speaker, allegedly bribed a fellow ruling party politician when Park was running for election as chairman of the Grand National Party, now called the Saenuri Party, in 2008.
In 2010, Park left his job as chairman of the party to become speaker of the National Assembly
Kim, a former senior political affairs secretary to Lee, allegedly was a key player in the scandal while he was helping Park work to win the chairmanship. Envelopes of money were allegedly distributed to Grand National Party politicians, a Yonhap report said in February.
Their indictments came after nearly two months of investigation by police which included Kim's resignation in February.
Kim also is a former section editor with The Chosun Ilbo newspaper.