US district judge Lucy Koh said it was time for the rivals to settle their numerous disputes, after a jury found that Samsung had copied crucial elements of Apple's iPhone and iPad.
Apple was awarded damages after 24 Samsung smartphone models were found to have infringed on Apple's patents earlier this year.
The South Korean company's lawyer said the amount should be slashed after being "reverse engineered" to see if it was legally arrived at by a jury.
Charles Verhoeven accused Apple of attempting to "compete through the courthouse instead of the marketplace".
But Apple's lawyer argued that more than $500m (£311.4m) should be added to the original amount - which it described as a "slap on the wrist".
Harold McElhinny also called for a permanent ban on the sales of eight Samsung smartphone models in the US, adding that the company would continue to fight Samsung until it "changed its ways".
During the hearing, the judge questioned the basis for some of the damages arrived at by the jury in August.
For example, she said the $58m (£36.1m) awarded over Samsung's Prevail smartphone - which was found to have used Apple's "tap-and-zoom" technology - could be too large.
"I don't see how you can evaluate the aggregate verdict without looking at the pieces," she said, adding: "I think it's time for global peace."
But the judge gave no indication on how she would rule on either the sales ban request or the amount of damages.
Since the summer's landmark trial, Apple's share price and market share has shrunk, as products by Samsung and other rivals grew in popularity.
Apple's shares have fallen by around 18% since the verdict on August 24, while Samsung's have increased by around 16%.
Judge Koh said she would issue a series of rulings over the legal issues raised in the coming weeks.
A further lawsuit involving the companies, over newer products, is set to come to trial in the US in 2014.
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