Not satisfied with the gun industry's response to demands for help ending an epidemic of gun violence, groups representing millions of workers are pressuring what they see as an even bigger change-maker: The funds that hold trillions of dollars in American retirement savings.

Their influence is far greater than many might think. About one-quarter of the world's 5,500 exchange-traded funds and 15 percent of all mutual funds invest in at least one company involved in the firearms industry, according to a report to be released Thursday by the corporate governance research firm Sustainalytics.

That has the potential to touch billions of dollars worth of retirement and pension savings. As of now, mutual funds hold more than $16 trillion in assets, and exchange-traded funds hold $3.5 trillion, according to the Investment Company Institute.

On Tuesday, the American Federation of Teachers asked the trustees of its pension funds to review its stock holdings and try to push fund managers to either shed investments in gun-makers and sellers or offer funds that have alternatives to firearms-makers. In doing so, the union is trying to "create accountability for what has become a high-risk investment," AFT President Randi Weingarten told CNBC.

AFT is the nation's second-largest teachers union, representing 1.7 million workers and $3 trillion of retirement savings. It is urging the pensions to drop investment managers that refuse.

"Failure to engage on this important investment risk issue should be considered as trustees review investment manager allocations going forward," it said in a report that accompanied a letter to the pension trustees.

Efforts to change rules about gun ownership and strengthen background checks and other safety measures came back into national headlines in February, when 17 people were killed in a mass shooting at a high school in Parkland, Florida. A student walkout supporting gun control was scheduled for Friday at schools around the country. On Tuesday, a student who survived the Parkland shooting called for a boycott of fund managers Vanguard and BlackRock.

Publicly traded companies involved in the gun industry, from firearms-makers such as Sturm Ruger and American Outdoor Brands and retailers like Dick's Sporting Goods, are not the biggest companies in terms of market value by far. But their ownership is widespread because of the boom in ETFs, which track stock market indexes.

Public school teacher pensions in 12 states have stakes in firearms-makers, largely through these funds, for example. BlackRock and Vanguard, managers of some of the most widely held ETFs, are among the largest shareholders of Sturm Ruger and American Outdoor Brands because of the funds.

Eleven ETFs track the S&P MidCap 400 Index, including BlackRock's $45 billion-asset iShares Core S&P Mid-Cap ETF. The index owns less than 1 percent each of Orbital ATK, which makes Bushmaster guns, and Olin, the maker of Winchester ammunition. And seven ETFs track the S&P's Small Cap 600, including BlackRock's $37 billion iShares Core S&P Small Cap ETF.

BlackRock has already offered some new ETFs that track the same indexes as its existing funds, minus gun-related company stocks, among other moves it is making to address the issue. Citigroup has restricted gun retailers who are its customers, and Bank of America said it will no longer finance companies that make assault-style rifles for civilians. Dicks said it won't sell guns to people under 21 years old.

Weingarten says the AFT tried unsuccessfully to talk to Wells Fargo about its business lending to the gun industry and will end a promotion offering Wells Fargo mortgages to teachers nationwide if it does not make contact soon. A Wells Fargo spokeswoman wasn't immediately available.

The AFT reached out to several fund companies, as well, including Voya, Dimensional Fund Advisors, Vanguard and Fidelity. The companies said they are talking to gun-makers and retailers about the risks posed by firearms. Invesco Advisors didn't respond, the AFT said.

Fidelity told the AFT it regularly engages with companies it invests in and evaluates whether those companies should stay in their portfolios.

If anything, the union and other groups, including faith-based organizations that have approached gun-makers with shareholder proposals this year, are raising awareness of the investment risk these stocks pose to pensions. Sustainalytics tracked the performance of gun-maker and retailer stocks and found that they all trailed the FTSE Global All Cap index for the last three years.

Combined, shares of Sturm Ruger, American Outdoor, Orbital ATK, Vista Outdoor and Dick's Sporting Goods were down 8.2 percent on a three-year basis versus the index's 20 percent gain.

In its report to the pensions, the AFT concluded, "Engagement is only meaningful if it yields changes in gun manufacturers' behavior that address core investor risks. If dialogue is insufficient to produce meaningful change, investment managers can and should vote their proxies in ways that reflect their concern and produce needed changes."

Correction: An earlier version misstated the day of the planned student walkout. It's Friday. The American Federation of Teachers is the nation's second-largest teacher's union. An earlier version misstated its status.