Saeb Erekat said he had passed on the message from Abbas to Putin during a visit to Moscow during which he met Russian Foreign Minister Sergei Lavrov.
"The letter asks President Putin to do what he can about the information we have that President-elect Donald Trump will move the embassy to Jerusalem, which for us is a red line and dangerous," Erekat said.
Today, the Grand Mufti of Jerusalem used his sermon at the Al-Aqsa Mosque compound to say the embassy move would represent an "assault" on Muslims across the globe.
The Palestinians regard east Jerusalem as the capital of their future state, while Israel proclaims the entire city as its capital.
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The city's status is one of the thorniest issues of the decades-long Israeli-Palestinian conflict.
Israel occupied the West Bank and east Jerusalem in 1967.
It later annexed east Jerusalem in a move never recognised by the international community.