"We shall do everything in our power to protect the rights of private investors in the Russian market," Chubais told a news conference. "We shall create conditions under which the market will push out the firms that issue bearers' shares."
Bearers' shares -- certificates whose holders are not registered with the company -- were technically outlawed in 1991.
But many companies, such as MMM and Khopyor-Invest, have issued securities that are the same as bearers' shares in all but name.
The securities, which carry the issuing company's name as the registered owner, have proved popular because they are easy to trade in a country where registering a share purchase usually requires traveling to a company's headquarters, be it in Moscow or Novosibirsk.
Chubais said the Securities and Exchange Commission, which he heads, has ordered all firms issuing such securities to register their holders and submit financial statements. Several were already doing so under the commission's guidance, he said.
"If such companies do not satisfy our requests, we shall take tough measures with them," he said.
Chubais singled out Khopyor-Invest as the only firm that had failed to provide his commission with details of its issues.
He said the company had attracted at least 57.5 billion rubles ($17.4 million) through share issues, but often did not register such essential data as shareholders' passport numbers.
That, in turn, left shareholders unable to prove ownership.
But Stanislav Tarasov, an aide to the president of the Khopyor financial group, said his company had received a letter from the Securities and Exchange Commission on Nov. 30, two days after the deadline to submit information.
"We are ready to answer all the questions the commission put in its request," he said, adding that Khopyor-Invest President Lev Konstantinov would speak on television Saturday to explain the company's position to shareholders.
Firuz Mansurkhodzhayev, head of the stock department at the Grant Financial Center, said that registration of shareholders could deal a serious blow to companies like Khopyor, because their shares' main advantage is that they are relatively easy to trade.
Other companies that have issued similar shares include Olbi-Diplomat, Kholding-Tsentr and the All-Russian Automobile Alliance.
"The shares will lose their only advantage: absence of fuss when registering," Mansurkhodzhayev said.
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