A group of large Wall Street law firms have banded together in an unusual bid to clamp down on a popular hedge-fund strategy aimed at squeezing more money from corporate takeovers.

Seven firms—including Cravath, Swaine & Moore LLP; Davis Polk & Wardwell LLP and Latham & Watkins LLP—are urging changes to rules governing an “appraisal,” a legal move in which stockholders who feel shortchanged by a takeover seek a higher valuation.

The firms made their case in a letter sent last week to a group of Delaware lawyers charged with recommending changes to the state’s corporate code, which governs the vast majority of U.S. public companies. A copy of the letter was reviewed by The Wall Street Journal.

The backdrop for the push is a sharp rise in so-called appraisal arbitrage, in which funds buy shares of a company on the brink of a sale and argue it is worth more than the takeover price. A record 33 public-company appraisal cases were filed last year in Delaware, and another 20 have been filed in 2015, according to a Wall Street Journal analysis. The targets are often private-equity-backed buyouts, with both of the largest such deals agreed to last year being challenged, those for grocery-store chain Safeway Inc. and retailer PetSmart Inc.

The law firms that signed the letter are some of the biggest names in mergers and acquisitions. Among their top clients are private-equity firms and target companies, which generally oppose appraisal arbitrage, as it threatens to complicate their deal making and make it less lucrative.

The issue is likely to come to a head by June 30, when the Delaware legislative session ends.

Delaware law allows investors seeking appraisals to buy shares right up until a deal closes, after the voting-eligibility deadline known as the record date. Critics argue the setup leads to an abuse of the appraisal right, which they say was meant to protect long-term shareholders from being taken advantage of in a merger. Also encouraging funds to mount the campaigns: They are guaranteed interest equivalent to 5.75% annually on the value of their stakes as the appraisal review takes place. That amount, established during a period of higher interest rates, is especially attractive amid today’s low yields.

The New York firms want to deny appraisal rights to funds that buy shares after the record date, according to the letter, which is also signed by Skadden, Arps, Slate, Meagher & Flom LLP; Simpson Thacher & Bartlett LLP; Sullivan & Cromwell LLP and Wachtell, Lipton, Rosen & Katz.

Such a change would “reduce the unseemly claims-buying that is rampant and serves no legitimate equitable or other purpose,” the letter said. The threat of an appraisal could lead acquirers to bid less upfront, knowing they may be forced to pay more later, the letter added.

The proposal goes further than one proposed by the group reviewing potential changes, whose recommendations are typically approved by the state legislature with little pushback.

A lot is at stake for the companies in question. Hedge funds including Fortress Investment Group LLC and Magnetar Financial LLC are seeking appraisal for some $230 million of shares in Dole Food Co., whose case is pending a decision. They are looking for nearly twice the $13.50-a-share the company’s chairman agreed to pay in his 2013 buyout of the firm, which was valued at $1.2 billion.

Some deals have attracted even bigger bets. Hedge funds including Third Point LLC have nearly $890 million tied up in claims challenging the roughly $8.25 billion buyout of PetSmart. It isn’t clear yet how much the funds will seek above the $83-a-share price a private-equity group agreed to pay for the company late last year.

Write to Liz Hoffman at liz.hoffman@wsj.com