Ashraf's lawyer submitted the letter of apology in the apex court on behalf of his client.
He apologised for asking the apex court to set up a commission to probe allegations of corruption in the power projects.
The Supreme Court had issued a notice to Ashraf, asking him to explain why he should not be charged with contempt of court for trying to influence the investigation into the power projects.
The rental power projects were mooted by the outgoing Pakistan People's Party-led government as a solution to Pakistan's crippling energy crisis.
The apex court had earlier ordered the arrest of Ashraf and other accused but the National Accountability Bureau said it had no evidence against the suspects to make arrests.
The charges against Ashraf date back to his tenure as Power Minister. The alleged corruption in the setting of the projects led to Ashraf being nicknamed "Raja Rental".
Ashraf suffered a humiliating defeat in the May 11 general elections in a parliamentary constituency in his hometown of Gujjar Khan near Rawalpindi.
The Federal Investigation Agency has barred Ashraf from leaving the country over the allegations of corruption in the power projects.