A reality TV hopeful and her husband who crashed a presidential dinner met President Barack Obama in the receiving line, the White House said Friday, as a "deeply concerned and embarrassed" Secret Service acknowledged its officers failed to check whether the couple was on the guest list.

The controversy over state dinner crashers, Michaele and Tareq Salahi, has prompted the White House to order a "full review" of the incident to find out how the Secret Service allowed such a security breach.

The White House said Friday it supported the Secret Service and its employees -- but also demanded answers.

"The White House asked the United States Secret Service to do a full review and they are doing that," White House spokesman Nick Shapiro said. "The United States Secret Service said they made a mistake and they are taking action to identify exactly what happened and they will take the appropriate measures pending the results of their investigation."

The White House has insisted that the Salahis were not invited to Tuesday's dinner for Indian Prime Minister Manmohan Singh, despite contrary claims by the couple and their lawyer.

"We have identified that a checkpoint of ours did not verify that these individuals were on the invite list," Jim Mackin, a Secret Service spokesman, told FoxNews.com. "The matter is currently being investigated."

Secret Service agents also met with the couple for questioning Friday at an undisclosed location in Virginia, the New York Post reported. 

Mackin said the Secret Service was considering turning the probe into a criminal investigation.

"As this moves closer to a criminal investigation there’s less that we can say," Mackin told the New York Post. "I don’t want to jeopardize what could be a criminal investigation. We are not leaving any option off the table at this point."

Some guests at Tuesday's dinner have already been interviewed in connection to the investigation, said Mackin.

The Secret Service has said President Obama was never in danger at the dinner, but declined to comment on whether anyone was screened for radiological or biological weapons.

Secret Service Director Mark Sullivan issued a statement Saturday, saying his agency took responsibility for the error.

"The preliminary findings of our internal investigation have determined established protocols were not followed at an initial checkpoint, verifying that two individuals were on the guest list," Sullivan said. "Although these individuals went through magnetometers and other levels of screening, they should have been prohibited from entering the event entirely. That failing is ours."

Sullivan said the agency that protects the president is "deeply concerned and embarrassed" that procedures were not followed.

Meanwhile, Rep. Pete King, R-N.Y., has called for a congressional hearing into the "shocking breach of security" at the White House dinner.

"As ranking member of the Homeland Security Committee, which has jurisdiction over the Secret Service, I am calling for a full investigation of how this shocking breach of security was allowed to happen and what is being done to make that it never happens again," King said in a statement released Friday.

FoxNews.com's Joshua Rhett Miller and The Associated Press contributed to this report.