Now Google and Yahoo will have to decide whether to move from test to broader partnership. Talks around a deal were active Friday, even as Yahoo and Microsoft were engaged in a last-ditch effort to come to an agreement, said a person familiar with the discussions.

For Yahoo, the idea of letting Google run some of its search ads is not new. Some shareholders and even some Yahoo executives have long favored it. By the company’s own reckoning, Google earns about 60 percent to 70 percent more on average for every search than Yahoo.

But before Microsoft made its offer, Mr. Yang and his team had repeatedly rejected the idea, saying search advertising was an essential part of the company’s long-term strategy. Instead, the company spent millions in improving its own search advertising system, called Panama, telling investors it was the right choice.

In a letter sent Saturday to Mr. Yang, Steven A. Ballmer, Microsoft’s chief executive, used precisely those arguments to emphasize why a search advertising partnership with Google was a bad idea. He also noted that it was one reason Microsoft decided to walk away from its offer, rather than initiate a proxy fight.

A partnership with Google “would fundamentally undermine Yahoo’s own strategy and long-term viability by encouraging advertisers to use Google as opposed to your Panama paid search system,” Mr. Ballmer said. “This would also fragment your search advertising and display advertising strategies and the ecosystem surrounding them.”

Yahoo and Google, however, are not talking about outsourcing all of Yahoo’s search ads to Google. Instead, they are considering a more limited partnership, under which Google would deliver ads only on particular searches for which the revenue difference is significant, according to people familiar with the discussions.

Analysts say such an arrangement could have multiple benefits. It would allow Yahoo to retain Panama and even use the extra revenue it receives from Google to invest in its own ad system. A limited partnership could help get around the antitrust scrutiny that a broader deal would most certainly face from regulators. The Justice Department has already begun asking questions about the companies’ relationships.