IBM is stepping up its fight against Amazon.com around cloud computing.

In an unusual move, IBM is launching a marketing campaign Monday that names Amazon as a rival and implicitly claims that IBM is the leader in the estimated $40 billion-a-year cloud-computing market. IBM rarely mentions competitors in any of its advertisements.

"Whose cloud powers 270,000 more websites than Amazon?" asks one print advertisement that will run in some major newspapers and business magazines. "If your answer is IBM, you're among the well informed. The IBM cloud offerings also support 30% more of the most popular websites than anyone else in the world."

The campaign, which will run in print, online and outdoors, highlights the growing stakes in the battle for the cloud as companies shift more of their technology purchasing dollars to renting computing over the Internet rather than buying and maintaining their own hardware and software. IBM would not disclose how much it is spending on the campaign.

The trend is a challenge to IBM, which has made billions of dollars installing, maintaining and upgrading computer systems for clients.

IBM recently lost a high-profile fight with Amazon for a $600 million contract to set up a cloud-computing system for the Central Intelligence Agency. The CIA surprised IBM when it picked Amazon, a win that could help unlock doors for Amazon with security-sensitive government agencies and commercial clients that have long been IBM's turf.

An Amazon spokesperson declined to comment on the IBM campaign.

IBM vice president of cloud services Ric Telford said IBM is launching the campaign largely because it recently completed its $2 billion acquisition of SoftLayer Technologies Inc.

SoftLayer rents space to clients on computers the clients don't own, an area dominated by Amazon. A client, for example, might put its database or website on computer servers operated by SoftLayer rather than buy its own.

Telford downplayed the loss of the CIA contract, claiming it was just one deal of many. "IBM wins more than it loses," said Telford, citing a 10-year, $1 billion cloud computing contract it announced this August with the Department of the Interior.

In the most recent quarter, IBM disappointed investors by falling short of Wall Street revenue estimates, but named cloud computing as a bright spot. IBM it generated more than $1 billion in cloud revenue, up 70% from a year earlier, and the first time IBM disclosed its cloud revenues.

In July, IBM said in a securities filing that the Securities and Exchange Commission was conducting an investigation into how the company reports cloud revenue. IBM said it is cooperating with the agency and follows accepted accounting rules.

– Greg Bensinger contributed to this report.