A surge in demand for its products yielded gains in income and revenue that were impressive even by Apple’s lofty standards. If there is a problem, it is that Apple is having trouble keeping up with some of the consumer demand.

Apple’s deal to make iPhones available on the Verizon Wireless network helped to lift iPhone sales, which more than doubled, to a record 18.65 million. The phones had previously been exclusive in the United States to ATT’s network, which many criticized for dropped calls.

“We did actually very well everywhere,” Tim Cook, Apple’s chief operating officer, said in a conference call with analysts.

Apple did not give specific numbers for iPhone sales for Verizon. But overall sales for both ATT and Verizon increased more than one and a half times in the United States compared with the quarter a year earlier.

The arrival of the iPad2, just before the quarter ended March 26, helped stoke tablet sales. Apple sold 4.69 million tablets in the quarter, including the iPad2 as well as the original version.

Consumers bought so many, in fact, that Apple is having trouble keeping up with the demand, prompting analysts to ask when Apple could ramp up production, and by how much.

Mr. Cook acknowledged the problem, calling it “the mother of all backlogs,” but he declined to be more specific about this quarter’s production. Apple’s Web site says there is a one- to two-week delay in shipping online orders. 

A. M. Sacconaghi Jr., an analyst with Sanford C. Bernstein Company, said that while Apple’s overall results were extraordinary, the number of iPads sold was a disappointment. “Whether Apple somehow messed up or was unable to secure components is an open question,” he said, but added, “It does sound like production will increase dramatically in the current quarter.”

To underscore his confidence, Mr. Cook reminded analysts that he approved Apple’s introduction of the iPad2 in 25 additional countries in late March and that the device will go on sale in 13 more countries next week.  

Even Apple’s MacBook laptop computers, an afterthought amid all the buzz around Apple’s phones and tablets, showed big gains after the introduction of updated versions during the quarter. Apple sold 2.75 million laptops, a 53 percent increase.

Sales of Mac desktop computers, however, fell 12 percent, to one million.

Apple’s computer sales defied an industrywide decline of 3.2 percent in computer shipments in the first quarter that was attributed to the disasters in Japan and a lack of better technology that would prompt consumers to upgrade, according to the research firm IDC.

Apple said it did not expect any significant impact on its supplies from Japan, where it gets hundreds of components.

The iPod, Apple’s music player, was among the few disappointments. Sales declined again, yet another indication of how smartphones, generally incorporating music players, are replacing single-function products. Sales of the iPod fell 17 percent, to 9.02 million.

Apple reported that net income in the second quarter rose 95 percent, to $5.99 billion, or $6.40 a share, from $3.07 billion, or $3.33 a share, in the year-ago quarter.

Revenue climbed 83 percent, to $24.67 billion, from $13.5 billion.

The results surpassed analysts’ expectations of $5.35 a share and revenue of $23.27 billion, according to Thomson Reuters.

Shares of Apple rose 3.1 percent, to $353.02 in after-hours trading after the announcement. In regular trading, shares had climbed 1.35 percent, to $342.41.

Mr. Cook has been in charge of Apple’s day-to-day operations since early this year after Steven P. Jobs, Apple’s chief executive and co-founder, took a leave of absence. Mr. Jobs, who has battled pancreatic cancer, said he needed to deal with health issues.

Asked about Mr. Jobs and his role at the company these days, Mr. Cook said: “He continues to be involved in major strategic decisions, and I know he wants to be back full time.”

Apple said it expected third-quarter revenue of around $23 billion and $5.03 a share. That is below analysts’ forecasts of $23.82 billion in revenue and $5.25 a share in income.

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