Market watchdogs and six major exchanges agreed new safeguards were needed to curb trading in plunging markets, an effort to address last Thursday's mysterious market free fall.

Securities and Exchange Commission Chairman Mary Schapiro met on Monday with the leaders of major stock and option exchanges, as well as the brokerage industry watchdog, the Financial Industry Regulatory Authority (FINRA).

As a first step, the parties agreed on a structural framework, to be refined over the next day, for strengthening circuit breakers and handling erroneous trades, Schapiro said in a statement that provided no further detail.

Regulators still have not pinpointed the exact cause of last week's 20-minute market roller coaster, when many stocks usually regarded as safe dropped precipitously for several minutes before recovering most of their losses.

One source said the general agreement on revamping market safety valves included a circuit breaker, or pause in trading, that would apply across all trading venues, if an individual stock falls sharply.

There was also agreement on updating the existing broad circuit breakers for severe market declines, said the source who requested anonymity because the talks are private.

Currently, if the market falls more than 10 percent in a day before 2 p.m. local time, a circuit breaker is triggered and shuts the market down for one hour. If the market falls more than 20 percent after 2.30 pm, the market shuts for the rest of the day.

Both the Dow Jones Industrial Average and Standard & Poor's 500 index never reached the crucial trigger point on May 6. The Dow fell as much as 9.2 percent and the S&P was off as much as 8.6 percent during the latter half of Thursday's trading day.

Schapiro held a two-hour Monday morning meeting with the leaders of the New York Stock Exchange, the Nasdaq Stock Market, BATS, Direct Edge, the International Securities Exchange and Chicago Board Options Exchange.

NYSE Euronext Chief Executive Duncan Niederauer, Finra CEO Richard Ketchum and others told reporters afterward that the discussions were constructive, without providing details.

U.S. Treasury Secretary Timothy Geithner urged a speedy response to last week's events when he met with the exchange heads on Monday afternoon, along with Schapiro and Commodity Futures Trading Commission Chairman Gary Gensler.

During the briefing, Secretary Geithner reinforced the need for a coordinated and timely response to help ensure the proper functioning of our markets, said Treasury spokesman Andrew Williams.

The SEC and other regulators are scheduled to appear with exchange executives before a House Financial Services subcommittee hearing on Tuesday.

STILL LOOKING FOR ANSWERS

Four days after the market plunge and quick rebound, regulators are still scrambling for answers, multiple sources familiar with the investigation said. The Dow Jones Industrial Average briefly went into a 1,000-point tailspin on May 6, rattling investors worldwide.

Stock exchanges have canceled trades on more than 200 largely NYSE-listed companies, upsetting investors in other companies who sold their stock at the bottom.

Sources familiar with the investigation say a good deal of attention if being focused on a popular futures contract linked to the S&P 500 index.

A massive $1 trillion rescue package to safeguard indebted European nations cheered investors on Monday, with U.S. stocks racking up their best one-day gain in over a year.

The CBOE VIX volatility index, known as Wall Street's fear gauge, fell 29.6 percent -- the largest percentage drop in its history -- to end at 28.84 after leaping to its highest level in more than a year on Friday.

One prevailing theory is that the sharp fragmentation of the U.S. stock marketplace and the accompanying patchwork of circuit breakers and safeguards exacerbated the market swoon.

That market fragmentation is also slowing down regulators' ability to piece together what happened, two sources familiar with the matter said on Monday.

The NYSE introduced a trading curb on its floor Thursday that forced most trading to all-electronic exchanges such as the Nasdaq Stock Market and NYSE Euronext's electronic Arca venue, which did not have similar curbs -- a lack of uniformity seen as having worsened the wider market's drop.

Now, regulators and the industry appear to be eyeing something like NYSE's system as a template for the whole marketplace.

The NYSE and Nasdaq, the two U.S. exchanges that list stocks, want to handle the reopening of markets following any future trading halts due to a circuit breaker, sources said.

TUESDAY HEARING

Due to appear at Tuesday's subcommittee hearing are NYSE Euronext Chief Operating Officer Lawrence Leibowitz, CME Group Inc Executive Chairman Terrence Duffy and NASDAQ OMX Group Inc Transaction Services Executive Vice President Eric Noll.

SEC's Schapiro, SEC division of trading and markets director Robert Cook, and CFTC Chairman Gensler will also testify.

The Senate, which is working on a broad rewrite of rules for financial markets and firms, has also gotten involved.

Senator Charles Schumer, a Democrat from New York, called on Monday for new systemwide circuit breakers that would put the brakes on free-falling individual stocks when a circuit breaker on one of the major exchanges is triggered.

Senate Banking Committee Chairman Christopher Dodd said the panel will meet as early as next week with regulators to discuss the causes of the market plunge.

(Reporting by Jonathan Spicer in New York and Rachelle Younglai in Washington, with additional reporting by Karey Wutkowski and Kevin Drawbaugh in Washington and Jonathan Stempel in New York; editing by Dave Zimmerman and Tim Dobbyn)

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