WASHINGTON — Two more Secret Service officers quit Tuesday over a sex scandal that tarnished the image of the elite protection agency, as President Barack Obama branded those involved as "knuckle heads."

A third agent had his security clearance revoked, a step likely to eventually see him dismissed, said Secret Service Assistant Director Paul Morrissey in a written statement.

Two other agents have been cleared of serious misconduct but will face "administrative" action, Morrissey said. Previously, one other agent had been cleared of misconduct.

The latest moves mean that nine Secret Service agents lost their jobs or will leave the Service over the sleazy episode which saw prostitutes invited back to their hotel earlier this month in the Colombian resort of Cartagena.

A total of 12 agents were investigated in the scandal, and all those cases have now been accounted for, following Tuesday's announcement.

"At this point, all twelve have either been cleared of serious misconduct, resigned, retired, been notified of personnel actions to permanently revoke their security clearances or have been proposed for permanent removal for cause," Morrissey said.

"The Secret Service is committed to conducting a full, thorough and fair investigation into this matter and will not hesitate to take appropriate action should any individual information come to light."

Twelve members of the military, including a member of the White House Communications Agency, are also being probed by the Pentagon.

The US agents and personnel had gone to Cartagena to prepare security for Obama's arrival for the Summit of the Americas and the affair morphed into a huge diplomatic embarrassment for the United States.

Obama earlier hit out at the US personnel who reportedly invited around 20 women back to the hotel after meeting up in a nightclub, but said their transgressions should not detract from the wider work of the Secret Service.

"These guys are incredible," Obama said, at a taping of NBC's "Late Night with Jimmy Fallon" show due to air later on Tuesday.

"They protect me, they protect our girls. A couple of knuckle heads should not detract from what they do. What were they thinking? I don't know. That's why they are not there anymore."

Officials said Monday that a probe conducted over the weekend by Obama's chief counsel had shown that no members of the White House staff, also in Cartagena prior to Obama's arrival were involved in the scandal.

Chuck Grassley, the top Republican on the Senate Judiciary Committee, said that the details of the White House report should be released.

"It seems to me the information ought to be public, particularly from a president who said three years ago when he was sworn in he was going to (have) the most transparent administration of any in history."

The White House has so far declined to release details of the internal probe.

"The White House Counsel's Office conducted a review -- there has been no credible, specific allegation of any misconduct by anybody on the White House advance team, White House staff," said Obama spokesman Jay Carney Tuesday.