WASHINGTON—A relaxed rule aimed at improving mortgage quality moved closer to approval after the Securities and Exchange Commission removed a key objection, according to officials familiar with the process.

The compromise approach is designed to assuage some regulators' concerns that the rule may not go far enough to prevent the type of lax underwriting that helped fuel the 2008 financial crisis, the officials said. The SEC won a concession in which U.S. policy makers are expected to agree to re-evaluate, and potentially adjust, the rule two years after its effective date and every five years after that.

The standard, expected to be made final in the coming months, is much looser than what was first floated in 2011, when policy makers said borrowers would have to put 20% down to get a loan or lenders would have to retain 5% of a loan's risk once it was packaged and sold to investors.

Under the revised approach, regulators wouldn't require a down payment and would include a broad exemption for banks and other issuers of mortgage-backed securities from having to retain a portion of the credit risk on their books.

Regulators have struggled to complete the rule in the face of concerns from the SEC, which objected to the loosened approach and said borrowers should be required to make some type of down payment to get a so-called qualified residential mortgage, said government officials close to the process.

That position put the SEC at odds with other regulators, who shared the housing industry's concerns that any down-payment requirement could crimp access to credit and impede the fragile housing recovery.

SEC Chairman Mary Jo White detailed her concerns about the rule, including the lack of a down payment, at a March 24 meeting at the Treasury Department with the heads of the other five agencies writing the rule, officials said. Ms. White's concerns were shared by the SEC's two Republican commissioners, Daniel Gallagher and Michael Piwowar, who wrote dissents to a version of the rule proposed last year.

Ms. White recently agreed to essentially adopt the revised mortgage rule without a down payment as long as regulators agree to re-evaluate the rule and ensure it is imposing restraint on the mortgage-backed securities market, these people said.

The move comes amid pressure from officials at other agencies, who argued a significant down-payment requirement could harm the fragile housing market, said people familiar with the matter. The Obama administration has begun trying to relax some of the postcrisis efforts to tighten mortgage-lending standards over concerns that the housing sector, traditionally an engine of economic recovery, is struggling to shift into higher gear. The overseer of mortgage firms Fannie Mae and Freddie Mac recently said the companies should make more credit available to homeowners, reversing previous directives to tighten credit.

The SEC's change of heart is the latest twist in a three-year battle over the 2010 Dodd-Frank mortgage rule, intended to improve the quality of loans by ensuring banks retain a stake in mortgages they make, package and sell to investors. Regulators have been struggling to define which types of high-quality loans would be exempt from the risk-retention requirement.

The original proposal three years ago sparked a backlash among housing-industry, affordable-housing and civil-rights groups, who banded together over shared concerns that a 20% down-payment requirement would end the dream of homeownership for many Americans.

Last year, regulators issued a new proposal with two options: Eliminate the down-payment requirement in favor of mortgage-lending rules written by the Consumer Financial Protection Bureau that required banks to verify a borrower's ability to repay a loan—or boost the downpayment requirement to 30%.

Most agencies, under pressure from lawmakers, the housing industry and consumer groups rallied around the first option. But the SEC remained the lone holdout, frustrating other government officials who had been working on the issue for years and had hoped the rules would be completed soon, according to people familiar with the process.

The agency's two Republican commissioners still are likely to vote against the final rule over concerns it won't impose enough discipline on Wall Street when packaging assets such as mortgages into securities.

Messrs. Gallagher and Piwowar also say it is inappropriate to adopt a rule essentially written by another agency—the CFPB—which isn't part of the mortgage-securities rule-making process. "We should not abdicate our responsibility to define [the mortgage standards] by surrendering the definition to the CFPB," Mr. Piwowar said in a statement.

Write to Alan Zibel at alan.zibel@wsj.com and Andrew Ackerman atandrew.ackerman@wsj.com