Here We Go Again: Apple Seeks $707 Million More From Samsung

the $1.05 billion it was awarded in August

According to a report from Reuters, Apple also has filed a claim for a permanent U.S. sales ban on several newer Samsung products that have launched since the two tech giants went to trial last year, including Samsung's Galaxy S III smartphone.

Samsung, for its part, has filed its own claim, requesting a new U.S. trial.

[Related: Study: Apple Gains Converts, RIM Makes Possible 'Fatal' Misstep ]

Apple is specifically seeking an additional $400 million in damages for Samsung's alleged design infringement, $121 million in supplemental damages for more recent Samsung product sales not addressed in the jury's initial deliberation, $135 million for willful infringement of its utility patents, and $50 million for prejudgement interest on damages through Dec. 31.

Apple said in its latest filing that these additional damages, totaling $707 million, would represent "a rational and fair effort to address Samsung's willful misconduct that has and will impose lasting harm on Apple."

Meanwhile, in requesting a new U.S. trial, Samsung claimed it was unable to present its full case against Apple during the first trial.

"The Court's constraints on trial time, witnesses and exhibits were unprecedented for a patent case of this complexity and magnitude, and prevented Samsung from presenting a full and fair case in response to Apple's many claims," Samsung said in its filing, according to Reuters.

Samsung also is claiming that many of the design patents called into question by Apple were too generic, targeting the basic rectangular shape of its smartphones and tablets.

"It is unfortunate that patent law can be manipulated to give one company a monopoly over rectangles with rounded corners, or technology that is being improved every day by Samsung and other companies," Samsung said.

The Korean tech giant has risen to become the largest mobile handset maker in the world, research firm Gartner reported last month, accounting for 21.6 percent of the global market in the second quarter. Nokia comes in at second with 19.9 percent and Apple is the world's third largest, accounting for 6.9 percent.

Apple and Samsung's patent war is being waged across the globe and has touched down in the U.K., Germany and the Netherlands.

PUBLISHED SEPT. 25, 2012