Consumer Watchdog is telling the White House that its cozy relationship with Google is inappropriate, given ongoing reviews by both the FTC and the Department of Justice.

The group, a vocal critic of Google, is asking White House Counsel Kathryn Ruemmler, who is responsible for overseeing ethics policy, “to rule that the president and other members of the administration must distance themselves from Google until the investigations are concluded,” according to a letter delivered to the White House on Friday.

Google is reportedly the subject of an antitrust investigation by the FTC, and Justice is reviewing its $400 million purchase of online advertising firm Admeld. In addition, Justice, the FDA and the Rhode Island U.S. attorney are reportedly looking into allegations that Google profited from selling online ads to illegal online pharmacies.

Despite those ongoing reviews, Google’s Executive Chairman Eric Schmidt and Vice President Marissa Mayer were guests at last month’s State Dinner to honor German Chancellor Angela Merkel.

“Allowing such executives to hobnob at a gala White House event inevitably sends a message that the administration supports them and undercuts the ability of federal investigators to proceed with their case in a fair and unbiased way,” reads the letter, signed by Consumer Watchdog President Jamie Court and Privacy Project Director John Simpson.

Schmidt has been friendly with President Barack Obama for several years, having advised his presidential campaign and transition team and now serving on the President’s Council of Advisors on Science and Technology. The warm relationship between Schmidt and Obama has been called into question before by Google critics who worried the search giant was getting special treatment in certain areas, such as broadband policy.

“Nonetheless, given the current circumstances, the president and top administration officials must distance themselves from Google until the serious allegations against the company are resolved,” the letter said.

Complicating the situation is Google’s refusal to send Schmidt or CEO Larry Page to testify at an upcoming hearing on competition. Sens. Herb Kohl (D-Wis.) and Mike Lee (R-Utah), chairman and ranking member of the Senate Judiciary antitrust subcommittee, said they may pursue a subpoena to force one of the Google executives to appear.

Google is in touch with the subcommittee and will “send them the executive who can best answer their questions,” spokeswoman Mistique Cano said Thursday.

Google did not respond to a request for comment on the Consumer Watchdog letter.

This article first appeared on POLITICO Pro at 5:38 a.m. on June 24, 2011.