NEW YORK/WASHINGTON (Reuters) - An influential U.S. senator wants to hold hearings into "disturbing" issues raised by secretly taped conversations between Federal Reserve supervisors and officials at Goldman Sachs Group Inc (GS.N), a bank the Fed was tasked with policing.

Elizabeth Warren, a Democrat on the Senate Banking Committee, on Friday called for hearings after portions of the recordings from 2011 and 2012 were made public. Fellow Democrat Sherrod Brown, also a committee member, called for a "full and thorough investigation" into the allegations they raised.

Carmen Segarra, a former New York Fed bank examiner who brought a wrongful termination lawsuit against her former employer, recorded the conversations and provided them to the investigative news outlet ProPublica and the public radio show "This American Life" to illustrate what she saw as an inappropriately close relationship between regulator and bank.

The tapes appear to show an unwillingness among some Fed supervisors to both demand specific information from Goldman about a transaction with Banco Santander (SAN.MC) and to strongly criticize what Segarra concluded was the lack of an appropriate conflict-of-interest policy at Goldman.

Political interest in the recordings could feed suspicion among Americans that little has changed on Wall Street since bank regulators failed to identify and stop the risk-taking that led to the 2007-2009 financial crisis and deep U.S. recession.

"When regulators care more about protecting big banks from accountability than they do about protecting the American people from risky and illegal behavior on Wall Street, it threatens our whole economy," Warren said in an emailed statement. "Congress must hold oversight hearings on the disturbing issues raised by today's whistleblower report when it returns in November."

Brown, in an email, said: "For too long, too many financial regulators have been too cozy towards the very industry that they are meant to police."

Segarra was fired after nearly seven months at the New York Fed as a so-called embedded supervisor at Goldman. She later sued the branch of the U.S. central bank for $7 million but the suit was dismissed in April for failing to state a claim that merited whistleblower protection, a decision she is appealing.

"The New York Fed categorically rejects the allegations being made about the integrity of its supervision of financial institutions," it said in a statement on its website.

On Friday, Goldman tightened rules on investments its bankers can make in individual stocks and bonds, a company spokesman told Reuters.

A source familiar with the situation said the bank's new conflict-of-interest rules on Friday were in the works for some time and were unrelated to the Segarra case.

Asked about the possibility of hearings, both the New York Fed and Goldman Sachs declined to comment.

Segarra stands by her allegations against the Fed, said Linda Stengle, her lawyer. "The audio on the tapes speaks for itself. Regardless of whether our case proceeds on appeal, we are gratified that Carmen is vindicated by the recorded words of employees of Goldman Sachs and the New York Fed," she said.

Segarra filed the wrongful termination suit in October, claiming she was fired after refusing to alter a critical examination of Goldman's legal and compliance units. In claims she repeated in Friday's media reports, she said superiors were too deferential to the bank and they pressured her to back down.

Some 46 hours of meetings and conversations were recorded, according to ProPublica.

In one conversation said to be among Fed examiners following a meeting with Goldman officials, one participant appeared concerned about pushing the bank too hard for details on the Santander deal.

"I think we don't want to discourage Goldman from disclosing these types of things in the future, and therefore maybe you know some comment that says don't mistake our inquisitiveness, and our desire to understand more about the marketplace in general, as a criticism of you as a firm necessarily," the unidentified examiner told his colleagues, according to a transcript provided by This American Life.

(Reporting by Jonathan Spicer and Emily Stephenson; Additional reporting by Amrutha Gayathri in Bangalore and Lauren LaCapra in New York; Editing by David Gregorio and Lisa Shumaker)