They asked the judge for calculators Tuesday to help determine how much Samsung owes for copying key features in 13 of its own phones and tablets sold in the US, after an earlier jury verdict in August 2012.
The deliberations are the latest stage in the series of ongoing legal battles between the two electronics giants, which has seen both sides seek sales bans against the other in Europe, the US, Australia and the far east.
Separately, Apple won an appeal court verdict on Monday which could mean that it will be able to enforce sales bans against a number of Samsung products for infringing functional patents - relating to how they work, not how they look - first used on the iPhone.
The jury is trying to decide the additional damages owing to Apple after about $400m of a $1.05bn award made by the previous jury was voided. Apple will definitely receive at least $600m after the trial.
Now though the jury must decide whether Apple should receive $52m - as Samsung contends - or $380m, as Apple says is the fair value of the damages it suffered for Samsung using features such as "pinch-and-zoom" for manipulating onscreen images and "bounce back" when scrolling past the end of onscreen lists.
The deliberation is in effect the curtain-raiser for another, potentially bigger trial between the two sides scheduled for March 2014 in California. There, Apple will argue that Samsung's existing products infringe its patents.
Judge Lucy Koh, the federal judge presiding over the patent trial, granted the jury's request before the smartphone rivals' lawyers delivered their closing arguments. The one-week trial is being held to determine damages for 13 of the 26 devices that an earlier jury said Samsung infringed on Apple's patents. At the same trial the jury turned down all of Samsung's claims that Apple infringed on its own patents.
The jurors deliberated for about four hours Tuesday and were scheduled to resume Wednesday morning.
Judge Koh vacated part of the previous jury's damages award because she determined that they had miscalculated the amounts owing for 13 of the 26 products in the original trial.
Apple's attempts to ban Samsung from selling some of the devices in question got a boost Monday. The US Court of Appeals for the Federal Circuit in Washington, D.C., ordered Koh to reconsider Apple's demands that some of the products a jury found infringed Apple's patents be barred for sale in the United States.
Koh in December turned down Apple, ruling that the company didn't prove that consumers bought Samsung devices instead of Apple devices because of the infringement.
The appeals court told Koh to apply a different legal standard that favours Apple's arguments. The ruling could come into play next year if Apple prevails at trial and seeks another sales ban on the newer products.
guardian.co.uk © Guardian News and Media Limited 2010
image: © Dominic Alves