By Justin Baer and Dawn Lim

Dec. 30, 2018 9:41 a.m. ET

Benjamin Nahum’s letters to corporate executives don’t set off alarm bells like those from billionaire investors like Carl Icahn or Dan Loeb.

Make no mistake, though, the Neuberger Berman Group LLC portfolio manager is increasingly borrowing a page or two from their playbook: He’s willing to scrap with the chief executives and board members of the small-cap companies whose shares his firm owns.

“When you get into one bar fight and you win,” Mr. Nahum said, “the next time you show up you get an even more serious audience.”

In the mutual-fund industry’s heyday, proxy fights and other activist tactics were considered unseemly, and often pointless. If a manager disapproved of managements’ actions, he or she would just sell the stock.

Today, they are taking on executives more frequently. Investors like Neuberger went public with their demands 60 times this year and in 79 instances in 2017, according to data tracked by Activist Insight Online. There were just 40 such public demands in 2014. Mr. Nahum launched one of Neuberger’s first major public brawls about three years ago, criticizing pay at UltraTech Inc. and calling for a shareholder vote that switched out some board directors.

These portfolio managers are also even more likely to push quietly for changes. They are asking companies to alter the makeup of their boards, run more environmentally friendly businesses or return more capital to shareholders, investors say.

A more confrontational tone with management is just one of many tactics active managers have tried to prove to their clients they’re worth their higher fees. As billions of dollars continue leave stock pickers for low-cost index funds, the industry finds itself in the fight for its future. To stem the tide, active managers are turning to strategies ranging from novel performance-fee funds to so-called alternatives such as private debt investments.

Stock pickers aren’t the only ones taking on management. The index-fund managers are trying to use their clout, too.

In his annual letter to fellow chief executives, BlackRock Inc.’s Laurence Fink said his firm would be more proactive. “The time has come for a new model of shareholder engagement,” he wrote. Ten months earlier, fellow passive juggernaut State Street Global Advisors launched a push to persuade companies to add more women to their boards.

These index heavyweights’ approach is different in several ways.

Active managers have teams of analysts who specialize in discrete industries, and can identify specific weaknesses holding back a company’s shares. Index investors instead prioritize a handful of issues and adhere to codes on how to effect change over the long haul. Bound by the indexes’ makeup, they can’t punish companies by dumping stock.

The large passive giants have also made a louder sales pitch.

“If Larry Fink is making statements saying companies have to operate in a certain way and index funds are becoming more vocal, active managers risk looking like the most passive money,” said Craig Wadler, a managing director who advises companies on activist shareholders at investment bank Moelis & Co.

Even if they don’t succeed at enacting change from companies, the index- fund managers succeed if they can erode a core reason clients were still willing to pay higher fees for active firms.

“I see the quants, the passives, the activists, hedge funds and private equity all raiding my client base,” said Mr. Nahum, who manages Neuberger’s U.S. Small Cap Intrinsic Value Fund. “We’re under attack and losing market share.”

Sweeping changes to the securities industry have altered the way companies interact with their shareholders, said Jim Rossman, head of shareholder advisory at Lazard Ltd. Electronic trading and the relentless concentration of stocks in the hands of fewer large shareholders minimized Wall Street’s role as gatekeepers to the corporate world, he said.

There are now fewer active managers holding sizable stakes in many companies. That’s made it harder for companies to freeze out those more critical of management.

“It took some time, but many of these active owners woke up to the fact that if they wanted to realize more value from their investments, they’d have to become more active owners,” Mr. Rossman said.

Lucian Bebchuk, a Harvard Law School professor, said it is still rare for a traditional manager to be openly critical of companies. “Like index funds, most of the major mutual fund families that focus on active funds display a deferential attitude toward corporate managers in their stewardship choices and activities,” he said.

There can still be consequences for rocking the boat. Managers don’t like to draw attention to investments that haven’t fared well, and that can happen when they tell the outside world a stock they’ve held for years is underpriced.

And while the Securities and Exchange Commission’s Regulation FD rules ban companies from doling out information selectively, managers might still get a cold shoulder from executives if they are too critical.

“You bear the mark of a troublemaker,” Mr. Nahum said. “You might get shut out of small group meetings.”

Mr. Nahum said that happened to him earlier this year we he tried to join an investor trip to software firm Verint Systems Inc. Verint had appointed a director proposed by Neuberger in early 2017. Mr. Nahum said he signed up for the outing with the Wall Street firm that had arranged it; later, he was bumped; the company wanted to give his spot to a newer investor. Verint officials did reach out, and within two weeks Mr. Nahum said he had a one-on-one meeting with the CEO.

A call to Verint’s investor-relations office wasn’t returned.

Write to Justin Baer at justin.baer@wsj.com and Dawn Lim at dawn.lim@wsj.com