If they decide to dump the investments, the process is more complicated than merely liquidating stocks. Fund managers are required by law to invest in profitable companies, often without any specific power to consider social or ethical issues.

The California State Teachers’ Retirement System announced Tuesday that it would review investments in the national and international firearms business.

That system had invested $600 million in the private equity firm Cerberus Capital Management, which on the same day put up for sale the gun maker known as Freedom Group International, manufacturer of the Bushmaster AR-15 military-style rifle, the weapon Adam Lanza used to kill 26 people at Sandy Hook Elementary School in Newtown, Conn.

The California retirement fund also owns shares of Sturm, Ruger & Co. and Smith & Wesson Holding Corp., two publicly traded gun manufacturers. Neither company responded to requests for comment Wednesday.

The New York State Teachers’ Retirement System holds nearly $3.4 million in Sturm Ruger & Co. and nearly $3 million in Olin Corp, which manufacturers Winchester arms. That’s out of total assets worth $38.1 billion. A spokesman for the teachers’ fund said the investment is “passive” and included in an index of funds.

Other gun makers, such as Sig Sauer and Colt, are privately held and even though regular investors generally can’t invest in private companies, pension funds often do.

In Pennsylvania, the teachers’ pension fund reacted quickly, contacting Cerberus about the Freedom Group even before the equity firm announced it was selling the gun maker.

The Pennsylvania fund has less than $2 million invested in Cerberus, and those holdings will soon be liquidated, an official said. Although the fund has no social investment policy, its board members became concerned after the Connecticut attack.

Freedom Group has lost money in four of the last five years but claims to be the biggest maker of “modern sporting rifles,” the industry’s term for military-style weapons. It estimates the market for those weapons has grown 27 percent a year from 2007 through 2011.

The company said it saw a “surge” of sales in 2009, Obama’s first year in office. FBI background checks are a rough proxy for gun sales. So far this year, the agency has already done 16.8 million, double the number it performed in 2003.

Sales of Smith & Wesson modern sporting rifles more than doubled to $61.3 million in the most recent quarter. The company announced record sales for the second quarter of $136.6 million, up 48 percent from a year ago.

Some public fund investors said the tragedy is forcing them to rethink where they put their money.

Matthew Sweeney, spokesman for New York City Comptroller John Liu, said the city is reviewing its holdings and “aggressively exploring all options,” including dumping the investments.

He advises the pension fund that covers city employees other than teachers, including police, firefighters and other city workers. New York City Mayor Bloomberg has for years been one of the nation’s loudest advocates for tighter gun control laws.

The city’s pension funds, worth $127.8 billion, have nearly $18 million invested in Brazilian gun maker Forjas Taurus, which sells the Taurus line of firearms in the U.S.; nearly $14 million in Olin Corp; $2 million in Sturm Ruger; and $1.7 million in Smith & Wesson.

Connecticut Treasurer Denise Nappier said the state’s $23 billion pension fund includes one direct link to a weapons manufacturer. It has stocks and bonds worth about $900,000 in Alliant Tech Systems, an aerospace defense company that supplies ammunition to law enforcement and commercial customers.

“My interest is ensuring that any company in which Connecticut pension funds are invested conducts its business consistent with our standards for responsible corporate citizenship — which includes considerations of public safety and the well-being of our children,” she said in a statement.

South Dakota holds no stock in firearms makers, but state Investment Officer Matt Clark said the state has no specific guidelines that would “impose our moral judgment over society’s.”

Funds do have some latitude, however. In the past, they have reduced investment in tobacco companies, divested from energy companies doing business with Iran after reports of genocide or dropped companies in South Africa when the country was segregated under apartheid.

When pension funds divest, fund managers give up the chance to change companies from within. DiNapoli, for example, has used his investment in Chevron Corp. to urge the company to settle an $18 billion court claim for environmental damage in the Amazon rainforest in Ecuador, which he said protected shareholders from risky company behavior.

Full divestment is rare and takes time. New York’s divestment in Iran took two years.

Some states — including Georgia, Mississippi, Louisiana, North Dakota and New Jersey — have no gun makers in their pension portfolios or they have little invested. Others, like Tennessee, leave investment decisions to index funds.

And some states are content to leave their investments alone, such as Arkansas and Texas.

In Texas, the teachers’ fund has a “small percent” of its $112 billion in firearms manufacturers. The fund constantly reviews all investments, but no special review is under way because of the shooting.

The Vanguard private money management firm said it would be difficult if not impossible to fulfill its fund’s obligations “while managing portfolios that reflect the social concerns of all of our shareholders.”

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Associated Press writers Mark Scolforo in Harrisburg, Pa.; Chet Brokaw in Sioux Falls, S.D.; James MacPherson in Bismarck, N.D.; Joshua Freed in Minneapolis; Betsy Blaney in Lubbock, Texas; Timothy Rogers in Raleigh, N.C.; Geoff Mulvihill in Trenton, N.J.; Erik Schelzig in Nashville, Tenn.; Jack Elliott in Jackson, Miss.; Kevin McGill in New Orleans; Gary Fineout in Tallahassee, Fla.; Chuck Bartles in Little Rock, Ark.; and Brock Vergakis in Atlanta contributed to this report.