(CNN) -- Apple co-founder Steve Jobs, who died Wednesday at 56, made the world "immeasurably better," the company's board of directors said in a statement.
The company also released an e-mail sent to Apple employees in which CEO Tim Cook announced Jobs' death, saying, "Apple has lost a visionary and creative genius, and the world has lost an amazing human being. Those of us who have been fortunate enough to know and work with Steve have lost a dear friend and an inspiring mentor. Steve leaves behind a company that only he could have built, and his spirit will forever be the foundation of Apple."
Cook's comments were repeated on the Apple website. Visitors were invited to share their "thoughts, memories and condolences" at rememberingsteve@apple.com.
There was no immediate word on any funeral services. Cook said the company is planning a "celebration of Steve's extraordinary life for Apple employees that will take place soon."
Jobs' family also released a statement through Apple, saying that Jobs "died peacefully today surrounded by his family."
"In his public life, Steve was known as a visionary; in his private life, he cherished his family. We are thankful to the many people who have shared their wishes and prayers during the last year of Steve's illness."
Apple's Steve Jobs dies
Jobs: Visionary in a black turtleneck
The family said a website will be provided for those wishing to offer tributes and memories.
"We are grateful for the support and kindness of those who share our feelings for Steve," the family statement said. "We know many of you will mourn with us and we ask that you respect our privacy during our time of grief."
Printed copies of a picture of Jobs -- posted on Apple's website announcing his passing -- appeared Wednesday night on a marble wall outside the Apple store on New York's Fifth Avenue, with notes written on them.
"We love you," one said. "RIP."
Outside the original Apple store in Cupertino, California, a makeshift memorial was created Wednesday, with people leaving flowers and other items. A bagpiper played as onlookers visited the site, some wiping their eyes.
Apple's board of directors said Jobs' "brilliance, passion and energy were the source of countless innovations that enrich and improve all of our lives. The world is immeasurably better because of Steve."
Jobs' greatest love was for his wife, Laurene, and his family, the statement said. "Our hearts go out to them and all who were touched by his extraordinary gifts."
"No words can adequately express our sadness at Steve's death or our gratitude for the opportunity to work with him," Cook told Apple employees. "We will honor his memory by dedicating ourselves to continuing the work he loved so much."
CNN's Susan Candiotti contributed to this report.
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