Jessica DeRubbio was 12 when her father, New York City firefighter David DeRubbio, died in the terrorist attacks of September 11, 2001.

“His hugs — I remember them so much,” Jessica, now 17, recalled in an audio memorial of her father. “When I used to hug him the whole world disappeared because he just would cover me and that would be it.” She also spoke of his lifelong dream of fighting fires in New York City.

As the interview boomed over a loudspeaker at a news conference yesterday with Mayor Bloomberg at the underground World Trade Center PATH station near ground zero at Vesey and Church streets, Jessica, her mother, and much of the audience fought back tears.

The memories of DeRubbio are among more than 300 personal histories of the infamous day recorded over the past year as part of an audio archiving project called StoryCorps.

Now, StoryCorps and the World Trade Center Memorial Foundation want to collect audio interviews about every one of the 2,979 people who died five years ago in the attacks and during the 1993 terror attack.

“It’s vital that we remember the individual lives of those we lost on that terrible morning,” the mayor said in prepared remarks yesterday.

As the fifth anniversary of the attacks approaches, the audio archiving project plans to extend hours the booth is open and provide reserved slots where families of September 11 survivors can honor the loved ones they lost.

While regular hours vary, the StoryCorps booths in Grand Central Terminal and the PATH station near ground zero will have extended hours on September 9, 10, and 11 between 10:30 a.m. and 7:30 p.m. Survivors, rescuers, and victims’ families can call (646) 723-7027 to schedule an appointment.

A copy of the sessions will be given to those who are interviewed and be archived with the Library of Congress. A few will air on public radio.