The US government's $1bn (£650m) fraud prosecution of Goldman Sachs has spurred calls for a wholesale crackdown on the opaque world of derivatives trading, with pressure mounting on the White House to deliver reforms forcing greater transparency in highly complex financial products.

President Barack Obama is engaged in a battle with Senate Republicans over an overhaul of financial regulation and has vowed to veto any bill that does not contain strong enough controls on derivatives.

The US government will face demands this week to use its 27% stake in Citigroup as a lever to extract more public information about trading. Citigroup's annual meeting will be held on Tuesday, and a shareholder group has urged the US treasury to vote its shares in favour of a resolution requiring greater disclosure from the bank on its collateral policy and speculative activities.

The Interfaith Center on Corporate Responsibility said that an "extraordinary opportunity" was being offered to send a message to Wall Street that "more derivatives disclosure is vital".

Alarm over misbehaviour in the derivatives sphere has been fuelled by a lawsuit taken out by the securities and exchange commission (SEC) against Goldman, which accuses the bank of colluding with a hedge fund, Paulson & Co, to stuff a mortgage-backed security package with specially selected, doomed home loans. While investors including Royal Bank of Scotland lost more than $1bn, the deal led to huge profits at Paulson & Co, which took a "short" position, betting on the transaction's failure. Both Goldman and Paulson & Co deny the allegations.

Analysts say that the case against Goldman could be the tip of an iceberg. A Dutch bank, Rabobank, accused Merrill Lynch over the weekend of a similar misdemeanour, claiming that Merrill marketed a collateralised debt obligation (CDO) while omitting to mention its relationship with a hedge fund betting against the product's success, resulting in a loss of $45m. Merrill called the allegation "unfounded".

Merrill, Citigroup and Deutsche Bank were the top three writers of mortgage-related CDOs in 2006 and 2007. All three banks saw their stock drop by more than 5% when the SEC announced charges against Goldman on Friday.

The US treasury secretary, Timothy Geithner, expressed optimism on Sunday that an agreement would be reached with congressional Republicans over financial reform: "I believe that we are very close on this."

Speaking on NBC's Meet the Press show, Geithner said that there had been "catastrophic failures of judgement" by people running top Wall Street banks and that reforms would make them pay: "Then taxpayers will not be on the hook for bailing out these large institutions from their mistakes in the future."

Oversight on derivatives trading has been a contentious topic for years. Advocates of light-touch regulation argue that the investors involved are sophisticated institutions that are savvy about the risks they are taking.

But the former US president Bill Clinton today expressed regret for listening to such sentiments. He said that he should not have listened to the former treasury secretaries Robert Rubin and Larry Summers, both of whom opposed tight protection when derivatives were gaining popularity during the 1990s.

"I think they were wrong and I think I was wrong to take [their advice] because the argument on derivatives was that these things are expensive and sophisticated and only a handful of investors will buy them," Clinton said.

The flaw in the argument, he added, was that "sometimes people with a lot of money make stupid decisions and make it without transparency".

Goldman's difficulties, which prompted a call from Gordon Brown for a UK inquiry today, are likely to lead to a flurry of lawsuits in the US from those who lost money in the credit crunch. Paul Geller of the law firm Robbins Geller Rudman & Dowd, which represents a union suing Goldman over mortgage losses, said: "Private lawyers are foaming at the mouth."

Among the casualties from Goldman's share slump on Friday was the billionaire stockpicker Warren Buffett, who saw his warrants in Goldman drop in value by just over $1bn.

Pressure on Wall Street banks to allow a clearer picture of the scope and complexity of derivatives trading has come from church groups and unions, which have taken a stronger line on reform than Democrat senators. Unions have blamed lobbying by the banks for legislators' reluctance to take a tough line. Republicans, hopeful of a backlash against healthcare reform in November congressional elections, now fear they will be punished for blocking calls for financial reform.

Meanwhile, the London-based Goldman banker Fabrice Tourre, accused by the SEC of being the mastermind behind the firm's alleged fraud, is becoming a cult figure. Several fan pages have been established to Tourre on Facebook, and for a time on Friday his name was the second-hottest search term on Google. So far, Tourre's only public comment was in response to a phone call from a Bloomberg reporter, to whom he replied: "I need to jump. Thank you, goodbye."

• This article has been amended. The currency conversion from $1bn should have read £650m.