A judge considering whether overturn Apple's billion-dollar patent damages victory over Samsung has called for a ceasefire in the ongoing war between the smartphone titans.

"I think it's time for global peace," US District Court Judge Lucy Koh said after legal teams from Apple and Samsung contested post-verdict motions in her Silicon Valley courtroom for several hours on Thursday.

"Let me hear if there is anything the court can do," she continued. "It would be good for consumers; good for the industry and good for the parties."

Samsung attorney Charles Verhoeven responded to the challenge by saying the South Korean consumer electronics firm was willing to negotiate a settlement with Apple but "the ball is in their court."

Apple attorney Harold McElhinny expressed no interest in working out a settlement, opting instead to urge Koh to back legal "remedies" daunting enough to dissuade a powerhouse like Samsung from ever copying an Apple gadget.

"It is the power of this court to establish a line and enforce it," McElhinny argued. "If you didn't see the same case that the jury saw, I am not sure how we get to resolution."

Verhoeven told Koh that Apple was engaging in "thermo-nuclear war", in reference to a Steve Jobs quote about Google's alleged copying of iOS, and choosing the court instead of the market as the battle ground.

Koh massaged her temples at times as she grilled rival attorneys for more than four hours regarding nuances of law and evidence underlying the slew of motions filed after the $1.049bn jury verdict three months earlier.

At times, she challenged Apple to convince her why the damages award for patent infringement wasn't excessive.

Koh adressed matters including how legal and sound the jury's calculations were, and whether the massive award should be reduced or even whether a new trial should be held just to recalculate damages.

"I have quite a number of questions, because there are so many issues and they are quite complex," Koh told the rival legal teams.

"I am planning to issue orders in installments, organized by subject matter," she added, explaining that her decisions on motions would be doled out in the weeks or months ahead.

Koh questioned the jury's mathematical and legal logic, targeting specific Samsung smartphones at issue in the case.

"I don't see how you can look at the aggregate verdict without looking at the pieces put together to make that verdict," Koh replied after Apple attorneys urged her not to try to figure out the jury's reasoning, device by device.

In an interview this week, Apple chief executive Tim Cook admitted his relationship with Samsung, one of his biggest component suppliers as well as main smartphone rival, was "awkward".