Samsung wants Apple to pay out €4.39 million for allegedly using technology it owns on the video-calling app 'FaceTime'.
The Korean giant has made its own demand for damages three weeks into a trial over claims it infringed on patents belonging to Apple.
The maker of the iPhone wants more than €1 billion.
Samsung has claimed that 'FaceTime' infringes a Samsung patent in relation to the compression of video before transmission over a mobile network.
Last November, Apple lost a court hearing related to the 3G technology they used in their iPhone 4 and early iPad 2 models.
The International Trade Commission ruled in favour of Samsung.
This latest patent issue between the two technology giants and surrounds a lawsuit brought by Apple over five separate patent infringements, including the "slide to unlock" feature that is prominent on both Apple and Samsung models.
All smartphone manufacturers are subject to a huge number of individual patents - most licensed in exchange for a tiny fee-per-product - to ensure all companies conform to universal standards.
In August 2013, the most high-profile American trial yet resulted in Apple being awarded over €750 million (on appeal reduced to around €460 million) when Samsung was found to be infringing a patent related to the basic design of Apple products.
And a related injunction saw Samsung's Galaxy Nexus devices being temporarily banned from being imported into the US.