Executives from the four most well-known search engines in the U.S. chatted about the future of the online advertising industry at Fortune’s iMeme tech conference in San Francisco.

And for the most part, the representatives of Google (GOOG), Yahoo! (YHOO), Microsoft (MSFT) and Ask.com, which is owned by Barry Diller’s IAC (IACI) got along nicely.

But there was a certain atmosphere of defensiveness, particularly among the executives of the three companies that are chasing Google, which has a commanding market share lead in search. Google’s representative also got a bit testy when competitors made comments about its market lead.

Jim Lanzone, the CEO of Ask.com quipped that his company would rather “have a slice of a watermelon than a whole grape,” when asked about his company’s single-digit market share in search. He added that the key to Ask’s success would be getting existing Ask users to use the site even more.

Yusuf Mehdi, the senior vice president and chief advertising strategist for Microsoft, conceded that his company, which trails Google and Yahoo in search, still has some catching up to do.

“There are areas where we are definitely coming from behind,” he said. But he stressed that Microsoft’s MSN has made some notable improvements in image search and that his company is “closing the gap” in keyword search.

Mehdi did take a not so veiled shot at Google though, which is known for offering large revenue commitments to advertisers in order to win deals. Mehdi said that  big guaranteed revenue deals are “bad for the industry” since it puts pressure on companies to hit certain traffic milestones.

Sheryl Sandberg, the vice president of global online sales and operations for Google, shot back by saying that Google comes to the table with “the largest ad network and a commitment to monetize” and added that she doubted too many of its customers were dissatisfied.

Sandberg also denied assertions that Google is becoming more of an enterprise software company, ala Microsoft.

Although the company now does offer products such as spreadsheets, calendars and other services that compete with Microsoft’s Office suite — Google also just announced the purchase of e-mail security firm Postini — Sandberg pointed out that her company is mainly offering these tools for free over the Web and is not putting together teams of consultants to sell software licenses.

And then there’s Yahoo. The company has come under a lot of criticism as of late for underperforming Google. In fact, Terry Semel is probably no longer the CEO of Yahoo because of this fact.

But Jeff Weiner, executive vice president of Yahoo, touted recent advances the company has made in ad targeting as a way to compete more effectively against the likes of Google. Yahoo has unveiled an updated search platform for advertisers called Panama as well as a new system for display ads (i.e. banners, video and other graphical ads) called Smart Ads.

“The holy grail for many of us in the industry is about getting the right offer to the right user at the right time. This has become a mantra,” he said.

Weiner also defended his company’s presence in social networking, an area that many people feel Yahoo lags behind Google’s YouTube, News Corp’s (NWS) MySpace and Facebook despite owning sites like Flickr, Jumpcut and Yahoo Answers. He called the company’s Yahoo Mail product “one of the largest dormant social networks” and that it would be Yahoo’s responsibility to activate it.

Whether Yahoo can wake up under new CEO Jerry Yang still remains to be seen. But it does seem like Yahoo employees are excited about the management change. Weiner called him a “fantastic person” to lead Yahoo and that his ascension to the top spot has energized the company.

Weiner also took a bit of a pot shot at Google when he said that the competitive nature of search has helped it win some new deals, including a distribution agreement with the online video joint venture of News Corp.’s Fox and GE’s (GE) NBC Universal, as well as a deal to sell ads for a consortium of newspaper companies.

But Google’s Sandberg didn’t seem too concerned about the threats from rivals. And she hinted that the company is looking to do much more than maintain its dominant position in search.

“We care about growth in users, growth in information and growth in our ability to provide users with information. What is the market for information? Search is a small place of the market to begin with.”