They were held last month during a protest against oil drilling in the Arctic.
The signatories – including Archbishop Desmond Tutu – described the charges of piracy as “excessive”.
But Vladimir Putin’s press secretary, Dmitry Peskov, responded that the president had no power to influence the courts.
The Greenpeace activists, who complain of being detained in harsh conditions, face up to 15 years in prison if convicted.
In the letter, which was released by Greenpeace, the laureates urge Vladimir Putin “to do all you can to ensure that the excessive charges of piracy against the 28 Greenpeace activists, freelance photographer and freelance videographer are dropped, and that any charges brought are consistent with international and Russian law”.
It is also signed by former East Timor President Jose Ramos Horta and Northern Irish peace campaigner Betty Williams.
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