"We are declining the statement of interest in this case," said State Department spokesman Tom Casey.
Under the US legal system, the administration can decide in cases of national strategic importance "to declare an interest" in a court case and call for a suit to be dropped.
The United States said earlier this month it was mulling whether to back a request from Abbas to avoid paying compensation to US victims of attacks in favor of a broader interest in promoting Israeli-Palestinian peace talks.
The Palestinians have argued that US financial aid would be diverted to compensation payments and leave the Palestinian Authority bankrupt.
However, in a letter to US District Court Judge Victor Marrero in New York, the Justice Department said it would not intervene but left open the possibility of intervening in other similar cases.
The Justice Department "will continue to monitor this and other cases like it," it said.
"The United States supports just compensation for victims of terrorism from those responsible for their losses and has encouraged all parties to resolve these cases to their mutual benefit," it said.
"At the same time, the United States remains concerned about the potentially significant impact that these cases may have on the financial and political viability of the defendants."
Victims' families have reportedly argued any US intervention to halt the cases would undermine the US administration's "war on terror."