Khamenei at the weekend had rebuked the deputies for their role in the squabbling that broke out in the February 3 impeachment session, during which President Mahmoud Ahmadinejad and speaker Ali Larijani got into verbal fight.
"For our part, we apologise for what happened ... during the impeachment," of the labour minister Abdolreza Sheikholeslam, said a statement signed by 265 members of the 290-seat parliament, media reported on Monday.
The parliamentarians emphasised that obedience to the leader, who had dubbed the impeachment as a "bad decision", was a "religious and legal obligation".
Following Khamenei's criticism, Ahmadinejad, the speaker and the judiciary chief Ayatollah Sadeq Larijani expressed "obedience" to him in separate letters, media reported.
The parliamentary row, which was broadcast on radio, came as parliament proceeded to impeach Ahmadinejad's labour minister for refusing to sack Tehran's ex-prosecutor Saeed Mortazavi as head of a wealthy social welfare organisation.
In that session, Ahmadinejad played a video recording which allegedly incriminates Fazel Larijani, a brother of both the parliament speaker and the judiciary chief, who is a direct appointee of Khamenei.
Fazel is shown in the clip as allegedly trying to bribe Mortazavi in exchange for political support from the parliament and the judiciary.
Larijani in response charged that Ahmadinejad was impeding justice by shielding his inner circle from judicial investigation.
Candidates seeking reelection and those who seek to become deputies, have to be vetted by the Guardians Council, whose members are appointed by Khamenei.
The rift between Ahmadinejad and the parliament and judiciary, two bodies which are dominated by conservatives critical of his administration, first surfaced in April 2011 when the president challenged a ruling by Khamenei, who has final say on all state matters.