Google may add a free service as early as this week that lets people send instant messages and make telephone calls through their computers.

The service will let users connect calls on their computers and talk with a microphone and speakers or a headset, six analysts including Piper Jaffray’s Safa Rashtchy in Menlo Park, Calif., said on Monday, citing speculation among industry contacts. The service eventually may be expanded to connect calls from computers to landlines, they said.

Adding Internet calling would help Google put pressure on Microsoft and Yahoo, which both offer similar services, as well as Skype Technologies SA and Comcast. The number of American users of Web-based phone service is expected to jump almost ninefold by 2009, letting Mountain View, Calif.-based Google bolster revenue by increasing the time users spend on the site.

“Google is looking to grab control of the PC desktop,” an analyst at market researcher Radicati Group in Palo Alto, Calif., Teney Takahashi, said.

The service, which also includes a feature to send written instant messages, will probably be free and may come out this week, Mr. Rashtchy said. Other analysts, including IDC’s William Stofega, expect the product to debut within the next month. A spokesman for Google, Nathan Tyler, didn’t return a phone call seeking comment.

Google, which beat competitors with services such as satellite mapping, is playing catch-up in computer-to-computer calling. Redmond, Wash.-based Microsoft in April released a version of its instant messenger that lets users make video calls.

Yahoo, the no. 2 search engine and most-visited Web site, already allows users to make phone calls between computers through its Yahoo Messenger software. The program also lets people exchange short text messages online.

Sunnyvale, Calif.-based Yahoo also is expanding its services, buying closely held Internet calling company Dialpad Communications in June. Yahoo executives said at the time they wanted to eventually connect calls between landlines and computers.

Like Yahoo, Luxembourg-based Skype offers an instant messaging tool that lets users hold voice conversations. Unlike instant messaging software from Microsoft and Yahoo, Skype’s program allows consumers to make calls to landline numbers for a per-minute fee. Customers can also pay a monthly fee for a phone number so people can call them from traditional phones.

More than 27 million people in America will make Internet calls by 2009, compared with 3.1 million this year, according to IDC in Framingham, Mass.

Cable companies such as Cablevision and Time Warner Cable have posted the biggest gains from the shift so far, winning customers from American local-phone carriers Verizon, SBC, and BellSouth, which together lost a total of more than 2 million local lines in the second quarter.

Web calling would be a “natural extension” to Google’s search engine, an analyst for the Boston-based research firm Yankee Group, Su Li Walker, said.

The company’s calling effort also may be coming too late. Yahoo’s instant messenger had 62.9 million users in May, compared with 141.8 million for Microsoft’s MSN Messenger and 54.9 million for AOL Instant Messenger, according to ComScore Networks.

“How do you create something that’s so compelling that people move from A to B?”an analyst at Forrester Research, Maribel Lopez, said.

That’s a problem Google has conquered in the past, Mr.Rashtchy said. “It won’t be a Skype look-a-like,” he added. They would come up with something that could be significantly better or integrated with other Google functions.”