Amazon said on Wednesday that it had added $2.75 billion to its investment in Anthropic, a start-up that competes with companies like OpenAI and Google in the race to build cutting-edge A.I. systems.

The investment comes six months after Amazon invested $1.25 billion in Anthropic, making the San Francisco start-up Amazon’s most important A.I. partner. Amazon said at the time that it had the option to bring its total investment to $4 billion. It had until the end of March to do so, according to financial filings.

Still, the additional investment shows the enormous resources tech companies are pouring into A.I. and is indicative of how much financial support Anthropic needs to keep pace with its peers.

“We believe our strategic collaboration with Anthropic will further improve our customers’ experiences, and look forward to what’s next,” Swami Sivasubramanian, an Amazon executive, said in a blog post announcing the investment.

While Anthropic gets closer to Amazon, it has shed a bulk of the holdings of a controversial investor. Last week, a federal judge granted approval for the bankrupt cryptocurrency exchange FTX to sell its stake in Anthropic. In 2021, FTX invested $500 million in the A.I. start-up, making up a stake of about 8 percent stake.

The value of that investment has since ballooned. Anthropic’s valuation tripled to $15 billion in just a year, The New York Times reported in February.

Anthropic was started in 2021 by a group of researchers from OpenAI, the company that created the ChatGPT chatbot. At the time, many of those researchers were concerned about OpenAI growing closer to Microsoft in a partnership eventually worth $13 billion.

Anthropic has steadily raised funds because developing the foundational systems for generative A.I. requires deep pockets, both to hire staff and to secure computing power.

But the Amazon investment in Anthropic is not just a simple equity stake. Like Microsoft’s investment in OpenAI, it includes gaining access to A.I. systems and commitments to provide computing power. But it stops short of the high-value acquisitions that could trigger an antitrust review. The Federal Trade Commission has begun an inquiry to see if these kinds of large A.I. deals hamper competition.

In a key part of the partnership, Anthropic agreed to build its A.I. using specialized computer chips designed by Amazon. Amazon has said it hopes Anthropic will help its efforts to meet the cutting-edge demands of A.I. as well as collaborate on designs of specialized chips.

Amazon also gets an early shot at making Anthropic’s A.I. models available to customers of its cloud computing service, and this month announced it would provide access to the most powerful Anthropic models, known as Claude 3.

The bankruptcy estate of FTX agreed to sell about two-thirds of its shares in the start-up for $884 million. The majority of the stake went to ATIC Third International Investment Co., a firm linked to a sovereign wealth fund in the United Arab Emirates.

Other buyers included the quantitative trading firm Jane Street and the Ford Foundation, a philanthropic group. Darren Walker, the foundation’s president, said in an interview that he viewed Anthropic as an important competitor to OpenAI.

“The fact that Anthropic has emerged and will be a strong competitor is a good thing for the markets, and it’s a good thing for the public and the public interest,” Mr. Walker said.

David Yaffe-Bellany contributed reporting.