SAN FRANCISCO -- Twitter shares hit a new high Tuesday, leading the way on a day of big gains for Internet stocks, as the microblogging service climbed to roughly twice the price the company set for its initial public offering last month.

Twitter has seen a dramatic rise in recent days, fueled by announcements about new targeted advertising services and a successful campaign to build viewership for a National Geographic TV special. But some analysts cautioned that Twitter has yet to show a profit and still faces many challenges.

"We don't question their potential, but we think it's going to take time to get to where the stock seems to reflect," said Scott Kessler, who follows Internet stocks for S&P Capital IQ. He suggested Twitter shares are rising in part because of investors looking for a "hot" company to buy into before the end of the year.

After gaining more than 9 percent Monday, Twitter saw its stock climb almost 6 percent Tuesday, hitting a peak of $52.58 before settling down to $51.99 at the close of trading. Twitter set its IPO price at $26 last month and gained more than 70 percent in its first day of trading Nov. 7.

Tuesday was also a good day for other Internet stocks: Facebook rose nearly 3 percent, Groupon jumped 4.4 percent and Yahoo (YHOO) gained almost 3.5 percent. Google (GOOG), Amazon and LinkedIn had smaller gains, while the tech-heavy Nasdaq index fell slightly.

Twitter shares have been climbing since last week, when it announced a major expansion of an advertising program known as "tailored audiences" that it began testing over the summer. The service promises to show ads on Twitter to users who have previously visited the advertiser's website.

Facebook and Google have had success with similar services, which use Internet "cookies" or other tracking information to find users who have already shown an interest in a particular company or product.

But Twitter's current stock price implies the company is worth 25 times the $1.1 billion in sales that analysts expect it will make next year. By comparison, Facebook and LinkedIn are trading at 12 to 13 times their estimated revenue.

Analysts are divided on the stock, with some issuing bullish reviews and others listing it with a "neutral" or "sell" rating. Evercore's Ken Sena raised his estimates and price target for the stock last week, saying he expects advertisers will be willing to pay higher rates for Twitter's "tailored audiences."

But S&P's Kessler said Twitter faces many challenges as it attempts to expand overseas and compete with bigger sites like Facebook. Twitter claims about 230 million users, while Facebook boasts 1.1 billion.

Contact Brandon Bailey at 408-920-5022; follow him at Twitter.com/BrandonBailey.