Microsoft this afternoon said it has restarted its pursuit of Yahoo. The company issued a statement:

"In light of developments since the withdrawal of the Microsoft proposal to acquire Yahoo! Inc., Microsoft announced that it is continuing to explore and pursue its alternatives to improve and expand its online services and advertising business. Microsoft is considering and has raised with Yahoo! an alternative that would involve a transaction with Yahoo! but not an acquisition of all of Yahoo! Microsoft is not proposing to make a new bid to acquire all of Yahoo! at this time, but reserves the right to reconsider that alternative depending on future developments and discussions that may take place with Yahoo! or discussions with shareholders of Yahoo! or Microsoft or with other third parties."

Update, 1:48 p.m.: Microsoft dropped its offer for Yahoo on May 3 after offering up to $47.5 billion to acquire the Internet giant in a deal that Yahoo's board of directors never warmed to. The company first began its pursuit of Yahoo in February as a way to quickly catch up with Google in the business of Internet search and online advertising.

Last week, billionaire financier Carl Icahn disclosed that he had purchased 59 million shares and options of Yahoo, taking about a 4.4 percent stake in the company, and forwarded a slate of candidates to replace the current board of directors at the company's July 3 stockholder meeting.

"It is quite obvious that Microsoft's bid of $33 per share is a superior alternative to Yahoo's prospects on a standalone basis," Ichan wrote in a letter to Yahoo Chairman Roy Bostock.

Microsoft provided no additional details on the nature of its new alternative transaction. Yahoo has been exploring the outsourcing of its U.S. search advertising to Google -- an arrangement that raised antitrust concerns and was one of the key factors cited by Microsoft CEO Steve Ballmer when he withdrew his offer three weeks ago.

Icahn, too, cautioned Yahoo's board against pursuing any "strategic alternatives" that would "impede a future Microsoft merger" without allowing shareholders to weigh in, at the least.

Yahoo's shares did not tumble precipitously in the days and weeks after Microsoft withdrew its bid, indicating the market's expectation that Microsoft would come back to the table. This despite repeated statements from Microsoft that the company had moved on.

Judging from this afternoon's statement, the company clearly has not. While Microsoft highlighted this undefined alternative transaction -- and said it has been proposed to Yahoo -- it also noted that an outright acquisition is still possible "depending on future developments and discussions that may take place with Yahoo! or discussions with shareholders of Yahoo! or Microsoft or with other third parties."

Translation: If Ichan successfully replaces Yahoo's board with a slate amenable to an acquisition, Microsoft could still be a buyer.

Microsoft concluded its short message today with this caution: "There of course can be no assurance that any transaction will result from these discussions."

As of 1:45 p.m., Yahoo had not issued a statement in response.

Update, 2:43 p.m.: Early indications are that the alternative transaction could involve the purchase of Yahoo's search business.

Kara Swisher quoted unnamed sources at both companies saying as much.

Google has continued to widen its already huge lead over both Yahoo and Microsoft in U.S. Internet search. In March, Google had 59.8 percent of the market, according to comScore. The company has an even more dominant share in some other markets, such as Europe, where more than 79 percent of March searches were performed using Google. Yahoo and Microsoft had less than 4 percent, combined.

Internet search is important because the majority of online advertising revenue currently comes through advertising sold next to search results.

Update, 2:57 p.m.: Microsoft just distributed an e-mail from Platforms and Services Division President Kevin Johnson putting the new Yahoo proposal in the context of the company's broader efforts to build a profitable business in online services and advertising. Read it here.