Neither of the top dogs from Apple Inc. and Samsung Electronics Co. Ltd. is backing down from the heated, multibillion-dollar patent battle between the two tech companies.

A few weeks ago, the trial began in a lawsuit in which Apple accused Samsung of purportedly copying its iPhone and iPad. Apple is seeking a sales ban as well as monetary damages. Meanwhile, Samsung claims Apple infringed several patents, including some for its key wireless technology.

Although the companies’ top executives participated in mediation before the trial started, U.S. District Judge Lucy Koh, who is overseeing the case, requested that the CEOs of both companies talk on the phone once more before the jury begins deliberations this week.

But yesterday, a Samsung attorney told Judge Koh that despite the phone chat, the CEOs weren’t able to come to a settlement.

Closing arguments for the case are today.

Read more InsideCounsel stories about Apple’s patent wars:

ITC to review patent ruling against Apple

Judge to hear arguments in Apple patent case against Motorola Mobility

Apple tries to bar sale of new Samsung phone

Apple gains ground in patent suit against Google’s mobile operating system

Mobile device makers wage antitrust wars

Samsung, Apple continue patent dispute

Samsung’s tablets may be banned in Germany

Samsung drops Apple suit