By Narottam Medhora and Stephen Nellis

(Reuters) - Microsoft Corp reported a 3.6 percent rise in fiscal second-quarter profit on Thursday, helped by growth in its fast-growing cloud computing business, but it saw a slight decline in margins in the unit that includes its flagship cloud platform Azure.

Shares of the world's biggest software company were up about 1.1 percent in after-hours trading.

Since taking charge in 2014, Chief Executive Satya Nadella has steered the company toward cloud services and mobile applications and away from its slowing traditional software business.

Gross margins for Microsoft's so-called "commercial cloud" business, which includes Azure and versions of its online Office 365 product sold to businesses, were 48 percent, said Chris Suh, head of Microsoft's investor relations.

That is down from last quarter's 49 percent but up from 46 percent a year ago, Suh said. The figure is watched closely by investors as a sign of the actual profit made of Microsoft's cloud products, which the company does not publish.

The Azure platform competes with cloud infrastructure offerings from market leader Amazon.com Inc, Alphabet Inc's Google, IBM and Oracle Corp.

"We're not at Amazon's margin today," said Suh. "Their infrastructure business is much larger. They have the benefit of scale. We track more like what Amazon was when they were closer to our size."

On the company's earnings conference call, Chief Financial Officer Amy Hood fielded questions from analysts about Azure-specific gross margins. She did not disclose a number but said there was a "material improvement" since last quarter.

Analysts also questioned Microsoft's practice of providing a combined gross margin for cloud infrastructure, which at other firms tends to have gross margins around 30 percent, and cloud software, which at other firms has higher margins of 70 percent or 75 percent. "I do think it will be a blend of those," Hood said.

But CEO Nadella emphasized that the company thinks of its cloud offerings as comprehensive lineup of both software and infrastructure, as it did with its historical business as a combination of products with different margins, like Office and Windows Server.

"We have a cloud strategy that is not just about infrastructure," Nadella said, pointing out differences with Amazon Web Services.

Revenue from Microsoft's 'Intelligent Cloud' business, which includes Azure, along with other data center software, rose 8.0 percent to $6.9 billion in the quarter. That beat analysts' average estimate of $6.73 billion, according to research firm FactSet StreetAccount. Microsoft's estimates for next quarter were $6.45 billion to $6.65 billion, only slightly hire than FactSet's $6.61 billion estimate.

In constant currency, Azure's revenue grew 94 percent year over year, a good pace but still the lowest growth rate since Microsoft began disclosing the number in 2015, and down from 121 percent the previous quarter.

"In general, as long as it's close to doubling right now, that's extremely solid performance given the business is getting big from an overall standpoint," said Cross Research analyst Shannon Cross.

Sales of Office 365 to businesses rose 49 percent, down from 54 percent in the previous quarter. As with Azure, Microsoft does not give an absolute dollar figure for Office 365 sales.

Sales in Microsoft's personal computing business, which includes its Windows software, once the bedrock of the company, fell 5.0 percent to $11.8 billion, slightly beating the rate at which personal computer sales fell in the quarter.

Along with his push into cloud and mobile, Nadella also orchestrated Microsoft's biggest acquisition, the $26.2 billion deal for LinkedIn, which closed last month.

LinkedIn contributed $228 million of revenue in the quarter, Microsoft said, but reported a net loss of $100 million, or one cent per share.

Excluding LinkedIn and some other items, Microsoft earned 84 cents per share in the quarter. That beat Wall Street's average estimate of 79 cents, according to Thomson Reuters I/B/E/S.

The company's net income rose to $5.20 billion, or 66 cents per share, in the quarter ended Dec. 31, from $5.02 billion, or 62 cents per share, a year earlier. (http://bit.ly/2kpo0w6)

Its adjusted revenue, excluding LinkedIn, was $25.838 billion, ahead of analysts' average estimate of $25.298 billion.

Microsoft's shares had risen 23.2 percent in the past 12 months, compared with the 20.7 percent gain in the broader S&P 500 index.

(Reporting by Narottam Medhora in Bengaluru; Editing by Sriraj Kalluvila and Bill Rigby)