Forty-two percent of voters said Medvedev's strength came from Putin's trust in him, while only 4 percent said his strength was his independence, according to the poll by the Levada Center, an independent pollster.
The survey of 1,600 people late last month had a margin of error of 3 percentage points.
Medvedev, the first deputy prime minister backed by Putin as the next president, is widely expected to win the presidential election on March 2.
His registration documents to run for president, submitted to the Central Elections Commission on Monday, will be considered by the commission on Friday or next Monday, commission member Nikolai Konkin told reporters Tuesday.
Medvedev, a lawyer by training, is expected to outline his campaign platform during a speech to the Congress of the Russian Association of Jurists in Moscow on Jan. 29, Kommersant reported Tuesday, citing sources in the association.
The report could not be confirmed Tuesday with Medvedev's office or the association, which counts Putin, the heads of all law enforcement and security agencies and ministries as well as all top judges as members.
Medvedev promised to unveil his campaign platform while visiting Murmansk on Friday. He said it would largely follow Putin's course over the past eight years.
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