The victims can sue for interest stemming from a six-to-nine-month period when they say payments to the fund were delayed, the court said on Thursday.
The decision reverses a lower court ruling that said the dispute over interest was a political question and not a matter for the courts, because US and German officials had negotiated the 1999 fund agreement.
The fund agreement - also known as the Berlin accords - was designed to end litigation in US courts filed by survivors and their heirs over unpaid labour, seized property and unpaid insurance policies.
The German government contributed $2.5billion to the fund, through an agreement forged between Bill Clinton, the former US president, and Gerhard Schroeder, the former German chancellor.
Seventeen large German firms - including Bayer AG, DaimlerChrysler AG, Siemens AG and Volkswagen AG - formed a pact called the German foundation industrial initiative to fund the industry contribution.
Burt Neuborne, a New York university law professor and a foundation trustee working on the lawsuit for the plaintiffs, said the companies agreed to contribute because they thought it was in the best interest of German industry and not necessarily because of their individual labour history.
He said: "There's no correlation between the companies that did this and the companies that were the worst of the slave-labour users."
He said that thousands of other German companies have also contributed and that the fund has distributed nearly all of its assets to over one-million claimants - 75 percent of them non-Jews.
Most of the claimants were from eastern Europe and were used as slaves or forced labourers.
The German firms argued that the agreement capped their interest payments at about $50million.
The six named plaintiffs - all Nazi camp survivors living in the US - argued that the figure represented the minimum amount of interest, not a cap.
Agnieszka Fryszman, the plaintiffs lawyer, said: "The people are old. It would be nice to get this over and done. The Holocaust ended over 50 years ago."
Through the fund, victims received US$500 to US$15,000 each for years of forced labour. Fryszman called the awards "symbolic" given that the claimants also endured starvation and many lost their families.
She said: "The survivors themselves want to hold the German companies to the letter of the agreement."
Neuborne said that the additional interest payments could be used to enhance awards to some claimants.
He said: "I'm going to urge that they use it to reinforce payments to any group that we feel hasn't gotten what they should, such as victims of medical experimentation."
He said that he expects the German companies to fight the additional payments.