The Apple and Samsung CEOs are meeting in the US today to attempt to settle their wide-ranging legal disputes surrounding their mobile device design and technology, reports Reuters.

Apple CEO Tim Cook and Samsung CEO Choi Gee-sung agreed to meet in a court-directed mediation in San Francisco after being ordered to do so by US District Judge Lucy Koh in April. Koh is overseeing one of the cases between the companies filed in the US District Court for the Northern District of California, the trial for which is scheduled for July.

Apple accused Samsung of “slavishly” copying the iPhone and iPad designs for the Galaxy range of smartphones and tablets, in April 2011. This triggered a number of similar legal actions from both companies that has now extended to ten countries and encompasses technology patents.

Court documents suggest the companies have already held one mediation session, although it is unclear whether the CEOs were present. A California court filing said the company bosses will be joined by the general counsels for their firms, while today’s session will be overseen by US Magistrate Judge Joseph Spero.

According to Reuters, Samsung’s head of mobile, JK Shin, said over the weekend that the company wants to resolve its dispute with Apple but added that there is “still a big gap in the patent war” between the companies.

Apple is also engaged in legal wranglings with Android phone makers HTC and Motorola Mobility.