Nasdaq has hundreds of penny stocks. Now it’s trying to purge them.

Nasdaq is taking steps to purge itself of dubious companies whose shares trade below $1 each, following criticism that the exchange has become home to hundreds of risky penny stocks.

Proposed rule changes released by Nasdaq on Thursday could accelerate the delisting of such companies as Bit Brother, a tiny Chinese blockchain company that became an embarrassment to the exchange during the past year.

Starting in 2020, Bit Brother carried out three reverse splits to keep its share price above $1, allowing it to maintain its Nasdaq listing, even as its share price sank more than 99% after adjusting for the splits. The stock drew attention in late December when it experienced a wild surge in trading volume, fueled by individual meme-stock investors and social-media buzz.

Bit Brother was finally delisted in March. But Nasdaq still took heat from brokers and investor advocates who say it lists too many other small, risky companies that don’t deserve the seal of approval that comes with an exchange listing.

“These are classic penny-stock companies that are often tied to pump-and-dump trading activity and other forms of market manipulation,” the electronic-trading firm Virtu Financial told the Securities and Exchange Commission in a petition filed in July.

Virtu urged the SEC to limit excessive reverse stock splits and to force exchanges to delist companies more quickly if their share prices fall below $1. Nasdaq-listed companies whose share drop below that level can currently stave off a delisting for more than a year, owing to various grace periods permitted under Nasdaq rules.

When a stock closes below $1 for 30 consecutive trading days, Nasdaq deems the company to be noncompliant and gives it 180 days to remedy the situation. After 180 days, if the stock hasn’t climbed above $1, the company can request another 180-day grace period. At the end of that second period, the company can still get a last-minute reprieve by appealing to a Nasdaq hearings panel. The delisting is stayed while the company awaits its hearing.

Some say those rules are lax, leading to a pileup of penny stocks on Nasdaq. On Wednesday, there were 523 stocks listed on U.S. exchanges that closed below $1 per share, of which 433 were listed on Nasdaq, according to Dow Jones Market Data. By comparison, there were fewer than a dozen sub-$1 stocks in early 2021.

The two proposed rule changes unveiled by Nasdaq on Thursday would tighten up some of the rules regarding sub-$1 stocks, though they don’t go as far as Virtu has demanded.

Under one of the proposed changes, companies that reach the end of their second 180-day grace period wouldn’t be able to postpone delisting by seeking an appeal. Instead, their shares would move to the over-the-counter market—a sort of purgatory where companies land after being delisted—while they await the appeal. Effectively, the rule change caps the amount of time that sub-$1 stocks can be listed on Nasdaq to roughly a year.

The second proposed rule change would speed up the delisting process for companies that recently did a reverse stock split. Under the change, if a company carried out a reverse split to prop up its share price, but then its stock fell below $1 within a year, Nasdaq would immediately send the company a delisting notice. The company could still appeal and remain listed for another 180 days.

Both rule changes must be approved by the SEC to take effect. In a regulatory filing posted on its website, Nasdaq said it was proposing the changes to protect investors, after observing a pattern of repeated reverse splits by troubled companies.

“Nasdaq believes that such behavior is often indicative of deep financial or operational distress within such companies rendering them inappropriate for trading on Nasdaq for investor protection reasons,” the exchange said.

In a reverse split, a company swaps multiple shares for one share, boosting the share price without changing the company’s market value. The maneuver is often viewed as a red flag by investors. Still, it has grown more common as speculative companies that went public in 2020 and 2021—a frenzied period for new issuance—have struggled to keep their share prices above $1.

Last year, exchange-listed companies carried out a record 495 reverse splits, according to S&P Global Market Intelligence. The pace has continued into this year, with 249 reverse splits in the first half of 2024, S&P data shows.

Write to Alexander Osipovich at alexo@wsj.com