By Brian Fung, CNN Business

(CNN) -- Twitter is actively exploring additional ways to make money from its users, including by considering a subscription model, CEO Jack Dorsey said Thursday. The move comes as Twitter suffers a sharp decline in its core advertising business.

"You will likely see some tests this year" of various approaches, Dorsey told analysts on an investor call held to discuss the company's second quarter earnings results. Dorsey said he has "a really high bar for when we would ask consumers to pay for aspects of Twitter," but confirmed that the company is seeking to diversify its sources of revenue in what are "very, very early phases of exploring."

Earlier this month, rumors flared about a paid Twitter option after the company posted a job opening focused on building a subscription platform codenamed "Gryphon." Twitter's stock surged at the time, signaling investor appetite for the company to find new revenue streams.

Shares of Twitter rose 4% in early trading Thursday following the earnings results.

Like its rival social networks, Twitter has focused on offering a free service and making money by allowing brands to target ads to its millions of users.

"We want to make sure any new line of revenue is complementary to our advertising business," Dorsey said. "We do think there is a world where subscription is complementary, where commerce is complementary, where helping people manage paywalls ... we think is complementary."

Twitter's growth plans are under close scrutiny as many advertisers pull back due to the pandemic. On Thursday, Twitter reported second-quarter ad revenues of $562 million, a 23% decrease compared to the same quarter a year ago.

The company has also been hit by advertisers participating in an ad boycott of social media, linked to the nationwide racial justice protests. But Twitter executives declined to say how much of an impact the boycott has had on Twitter's business.

Twitter's earnings report follows what Dorsey described as a "tough week" in which the company scrambled to address a massive hack that compromised numerous verified accounts, including those of Barack Obama, Joe Biden, Elon Musk and Jeff Bezos.

On the eve of its earnings results, Twitter announced that dozens of accounts -- including one elected official in The Netherlands -- may have had their direct messages accessed by hackers as part of the security incident.

Dorsey apologized on the conference call Thursday for last week's massive security breach, saying "we fell behind" on the company's security obligations.

"We feel terrible about the security incident," he said. "Security doesn't have an end point. It's a constant iteration ... We will continue to go above and beyond here as we continue to secure our systems and as we continue to work with external firms and law enforcement."