As Apple Inc. was being targeted by an onslaught of negative advertising from arch-rival Samsung Electronics Co., the iPhone maker was racing to figure out how to fight back, according to evidence presented at a $2 billion patent trial.

Jurors in the companies’ second U.S. trial over smartphone technology today saw e-mails and heard testimony showing that Apple executives last year weighed dropping the firm that has exclusively handled its advertising for 17 years to better respond to a blitz by Samsung mocking the iPhone.

The evidence introduced in federal court in San Jose, California, is part of Samsung’s attempt to demonstrate that its products and marketing, and not the alleged infringement of Apple’s patents, drove sales of Galaxy smartphones and caused iPhone sales to decline.

The world’s top two smartphone makers have fought in courts on four continents to dominate a market that was valued at $338.2 billion last year, according to data compiled by Bloomberg. Samsung had 31 percent of industry revenue, compared with 15 percent for Apple, whose share of the market has shrunk as the touch-screen interface has become commonplace and Samsung, LG Electronics Inc. and Lenovo Group Ltd. have introduced lower-cost alternatives.

The evidence shown in the case illustrates how concerned Apple was about Samsung’s advertising and the behind-the-scenes scramble under way to respond.

Other documents shared with the jury today reveal Apple’s concerns last year about slowing iPhones sales. In April 2013, as Apple was being targeted by ads, an internal company presentation outlined how sales growth was slowing as a result of less expensive and bigger-screen phones from competitors, including Samsung, using Google Inc.’s Android operating system.

“I now have Apple board members asking ‘what is going on with advertising and what are you doing to fix it,’” Philip Schiller, Apple’s senior vice president of marketing, said in a Jan. 31, 2013, e-mail to James Vincent at TBWA/Chiat/Day’s Media Arts Labs unit, the ad agency.

Apple’s steady use of the same agency for almost two decades is a rarity in an area where companies often switch to get an injection of new ideas. Working with company co-founder Steve Jobs, the advertising team helped develop campaigns such as the “Crazy Ones” that associated Apple with historic figures such as Albert Einstein, as well as the “I’m a Mac” and “There’s an app for that” pitches.

The relationship frayed once Samsung began attacking Apple. Schiller said in January 2013 that instead of coming up with great iPhone ads, the advertising agency was criticizing Apple as “beleaguered” and needing to change practices such as its corporate governance, according to an e-mail presented today. Schiller said the agency compared Apple’s position in 2013 to 1997, the year Jobs returned as chief executive officer and the company was near bankruptcy and its image in tatters.

After Schiller raised the idea of getting a new agency, Apple Chief Executive Officer Tim Cook, who took over after Jobs died in October 2011, responded: “If we need to do this, we should get going.”

In another e-mail displayed for the jury, Schiller, who was on the witness stand for a second day, was discussing with Vincent a Wall Street Journal article from January 2013 titled “Has Apple Lost its Cool to Samsung?”

Samsung’s campaign, including some ads that ran before last year, mocked loyal iPhone users for waiting in line to buy new models and Apple for touting features that were already available in other smartphones including Samsung’s Galaxy.

“We have a lot of work to do to turn this around,” Schiller wrote Vincent.

“We feel it too and it hurts,” Vincent responded. “We understand the really critical nature of this moment. This perfect storm of factors is driving a chilling negative narrative on Apple.”

Schiller messaged Vincent about an ad Samsung aired before the 2013 Super Bowl.

“It’s pretty good and I can’t help but think ‘these guys are feeling it’ (like an athlete who can’t miss because they are in a zone) while we struggle to nail a compelling brief on iPhone,” he wrote on Jan. 31, 2013. “That’s sad because we have much better products.”

In a 2012 trial, jurors in the San Jose courthouse found that Samsung infringed six of seven Apple patents at issue and awarded the Cupertino, California-based company $1.05 billion, while rejecting Samsung’s infringement claims against Apple. Damages were later reduced to $930 million after a retrial.

In the second case, Apple claims that 10 Samsung products, including the Galaxy S3, infringe five different patents. Samsung alleges that eight Apple products, including the iPhone 5 and versions of the iPad and iPod, infringe two patents. Samsung, based in Suwon, South Korea, seeks about $7 million in damages, according to a court filing.

The case is Apple Inc. v. Samsung Electronics Co., 12-cv-00630, U.S. District Court, Northern District of California (San Jose). (Bloomberg)