Two of the world’s biggest currency-trading platforms plan to restrict a controversial industry practice in which banks can pull out of trades at the last moment if the market moves against them.

Thomson Reuters Corp. and BATS Global Markets Inc. will limit the practice, known as “last look,” on their platforms in coming weeks, in a move aimed at increasing transparency in the foreign-exchange market.

The change comes amid a broader shake-up of the trading industry prompted by concerns about traders’ efforts to manipulate a range of financial markets. Markets for precious metals, interest rates, stocks and currencies have all come under scrutiny from regulators in recent years because of allegations of inappropriate behavior.

Regulators in the U.K., the global hub for foreign-exchange trading, are expected to report next month on their own review into the supervision and transparency of some markets, including the foreign-exchange market. The so-called Fair and Effective Markets Review, or FEMR, specifically asked asset managers and other bank clients about their views on last look.

While some foreign-exchange platforms already don’t permit last look, it is still allowed on some large venues, including Hotspot, owned by BATS; and FXall, owned by Thomson Reuters. Hotspot and FXall account for about 25% of clients’ electronic forex trading, according to financial-industry consultants Greenwich Associates.

The last look practice is a legacy of over-the-phone currency trading, when traders would take a final check of the market before executing an order. It has survived even as foreign-exchange trading moved onto electronic platforms, leaving banks with the option to back out of an order after it was accepted by a client.

Thomson Reuters and BATS plan to tighten the time frame for canceling quotes and introduce a minimum acceptance rate banks have to respect.

Phil Weisberg, global head of foreign exchange at Thomson Reuters, said last look requires “more clarity.” Some clients don’t understand “the rules of engagement with the bank” and “are confused about trading protocols,” he added, referring to the exact conditions banks have to respect on the execution of each specific trade.

William Goodbody, head of FX at Hotspot, said, “Last look is a widely used practice in the industry. To make it work, it needs a clear set of guidelines.”

In June 2014, the U.K. Treasury, the Bank of England and the Financial Conduct Authority, the U.K.’s financial watchdog, launched the FEMR to consider ways to improve the supervision and transparency of some markets. FEMR findings, due to be released on June 10, are expected to establish rules on the execution of currency trades.

Foreign exchange is a highly unregulated market, compared to stock trading, as currencies aren’t traded on exchanges.

Banks’ foreign-exchange trading clients are likely to welcome the move to curb last look, said Kevin McPartland, a principal at Greenwich Associates.

“Giving market participants more visibility into where, how and with whom their orders are executed is a good thing,” Mr. McPartland said.

Javier Paz, a senior consultant at Aite Group, said last look echoes the equity-market practice of “spoofing,” an illegal strategy in which traders place orders they don’t intend to execute to move the market to their advantage.

But there are also some significant differences, he said. In spoofing, a trader places an offer to buy or sell, then cancels it quickly, whereas in last look, there’s always a client willing to execute one side of the trade, Mr. Paz said.

Write to Chiara Albanese at [email protected]

The Justice Department has begun looking into a common practice in foreign-exchange markets that allows banks to back out of unfavorable trades at the last moment, a person briefed on the matter said.

Prosecutors, along with the Securities and Exchange Commission, have asked Barclays Plc for information related to its electronic-trading platform, which contains a program that allows traders to take a “last look” at an order before executing it, according to the person, who asked not to be named because the matter isn’t public.

Prosecutors’ interest in the last-look practice has grown out of a broader investigation into the manipulation of benchmarks and client orders in the $5.3 trillion-a-day currency market. The inquiries follow an investigative path laid out in recent months by Benjamin Lawsky, New York’s banking regulator.

Barclays said earlier Tuesday that it set aside an additional 750 million pounds ($1.2 billion) to cover the cost of settling the currency-rigging investigation, bringing its total expected cost to about 1.25 billion pounds.

The last-look option is a vestige of the early computer era when the time lag between an order being entered at one bank and confirmed at another was long enough to expose the market maker to unpredictable price fluctuations. As that lag tightened, banks retained the right to halt currency trades on a last-look basis.

Critics of the practice say it’s obsolete and can harm investors.

“Last look is a hangover from a technology problem that no longer exists, yet still allows traders to reject trades and re-quote orders to the disadvantage of clients,” David Mercer, chief executive of LMAX Exchange, a forex trading platform, said in a Feb. 20 statement.

BlackRock Inc. said last month that last looks can cause market participants to experience so-called phantom liquidity where prices that appear to be available suddenly disappear, in response to the Bank of England’s Fair and Effective Markets Review. Making completed trades available and transparent would make the market better, BlackRock said.

“These developments, would in our view, facilitate fairer outcomes for end investors and increase market effectiveness and efficiency,” BlackRock said.

It isn’t clear whether the Justice Department’s review of last-look practices will lead to a new front in its forex investigation. The SEC is exploring whether any elements of the practice violate disclosure laws, another person briefed on the matter said.

Peter Carr, a Justice Department spokesman, declined to comment on any inquiry specifically into last-look practices, as did Florence Harmon of the SEC.

Until now, regulators in the U.K., Switzerland and the U.S. have been primarily focused on manipulation of benchmark currency exchange rates by traders at some 30 global banks, with an emphasis on collusive behavior. The last-look review indicates that regulators and prosecutors are turning their focus to established practices that could make markets unfair.

The prosecutors’ request appears to bolster a line of inquiry opened up by Lawsky, superintendent of New York’s Department of Financial Services, who said last month that he was looking into the practice.

In its annual report released Tuesday, Barclays said that various “regulatory and enforcement authorities,” including the Justice Department, SEC and Lawsky’s agency, “are investigating a range of issues associated with Foreign Exchange sales and trading, including electronic trading.” Kerrie Cohen, a spokeswoman for Barclays, declined to comment.