The bridge would span the 4.5-kilometer Strait of Kerch, which separates Ukraine and Russia, an estimated $3 billion project that has been under discussion for a decade.
Russian troops have fanned out across the Crimean peninsula in recent days, seizing strategic locations and reportedly digging trenches at an emerging border with Ukraine.
Ukraine’s acting president and prime minister have accused Russia of invading their country while international leaders have condemned Moscow’s actions as an attempted annexation of Crimea.
Medvedev told a Cabinet meeting that he had signed an order creating a subsidiary of state-owned road builder Avtodor that will be responsible for implementation of the bridge project. This step would move the project to a more practical phase, he said.
The announcement is the latest in a series of measures that look set to make Crimea more economically dependent on Russia.
Russian Finance Minister Anton Siluanov said Monday that the regional budget of the Crimean government was running a 35 billion ruble ($1 billion) deficit and that Russia would develop a plan of financial aid for the region by the evening.
Russia agreed to provide $15 billion in financial aid for the Ukrainian government of President Viktor Yanukovych before he fled into exile last month as violent clashes between riot police and anti-government demonstrators claimed 88 lives and left hundreds injured.
Moscow has now frozen that financial support, saying that it wants to understand more clearly who is in control of the government in Kiev.