Russia's foreign ministry is calling on Ukraine to become a federal state and call fresh elections.
In a statement posted on Monday the ministry urged Ukraine's parliament to call a constitutional assembly which could draft a new constitution to make the country federal, handing more power to its regions.
The foreign ministry said the proposals are part of its efforts to ease the tensions in Ukraine by diplomatic means.
Moscow insisted that Ukrainian regions should get broader autonomy and that the country should adopt a "neutral political and military status."
Crimea's parliament on Monday declared the region an independent state, after its residents voted overwhelmingly to break off from Ukraine and seek to join Russia.
In a sign of rising tensions following the Sunday referendum that called for annexation to Russia, the Ukrainian parliament also approved the president's order for a partial armed forces mobilization of up to 20,000 people and said that all Ukrainian state property on the territory of the Black Sea peninsula will be nationalized and become the property of the Crimean Republic.
The referendum is not recognized by the West, and the United States and the European Union are preparing sanctions against Russia, whose troops have been occupying Crimea for several weeks.
Crimean lawmakers have asked the United Nations and other nations to recognize it.
A delegation of Crimean lawmakers is set to travel to Moscow Monday for negotiations on how to proceed further. Russian lawmakers have suggested that formally annexing Crimea is almost certain.
The Kremlin clearly put the issue on a fast track. Both houses of parliament were set to gather for a joint meeting in the Kremlin on Tuesday to hear President Vladimir Putin's address on the subject.
In Kiev, the national parliament approved acting President Oleksandr Turchynov's call for a military mobilization that would include 20,000 volunteers with previous military experience, and reservists. Ukraine recently formed a national guard also about 20,000-strong.
Turchynov said the order was necessary "considering the continuing aggression in ... Crimea, which Russia is trying to disguise with a large farce called `referendum,' which will never be accepted by Crimea or the whole civilized world," he was quoted as saying by the Intefax news agency.
Russia is expected to face strong sanctions Monday from the U.S. and Europe over backing the Crimean referendum, which could also encourage rising pro-Russian sentiment in Ukraine's east and lead to further divisions in this nation of 46 million. Residents in western Ukraine and the capital, Kiev, are strongly pro-West and Ukrainian nationalist.
Russian forces effectively took control of Crimea late last month after Russia-friendly President Viktor Yanukovych fled the country in the wake of months of protests.
Ukraine's parliament endorsed on Monday a plan to mobilise 40,000 reservists to counter Russia's "blatant aggression" in Crimea and guard against what a senior official described as further incursions in the south and east of the country.
Andriy Parubiy, Secretary of the National Security and Defence Council, told parliament that 20,000 reservists would be deployed as part of the armed forces and the other half would serve in a newly-created National Guard.
Crimea was brought under Russian control earlier this month and in a referendum held on Sunday, more than 96 percent of voters were officially said to have backed a proposal to secede from Ukraine and become part of Russia.
"What has taken place is a seizure, blatant aggression, the seizure by Russia of parts of the territory of Crimea and the city of Sevastopol," Parubiy told the chamber before the vote.
"We now have grounds to state that the measures being taken today are enough to prevent a repeat of the Crimean scenario in Ukraine's southeastern regions."
These regions include Donetsk and Kharkiv, two cities which have seen unrest and clashes between pro-Russian and rival demonstrators, as well as Odessa, a Black sea coastal area to the northwest of Crimea.
A total of 275 members in the 450-seat assembly backed the measure. About 30 deputies in the chamber refused to vote.
A decree by acting President Oleksander Turchinov called for mobilisation within 45 days and provided for complete financing and provision of facilities for the reservists.
Russian President Vladimir Putin has said he reserves the right to defend the rights of Russian-speaking Ukrainians in southern and eastern Ukraine following the installation of a pro-Western government in Kiev last month. However, his foreign minister has said Moscow has no plans to invade these areas.
Violent pro-Russian demonstrations have taken place in eastern Ukrainian cities, disturbances blamed by authorities in Kiev on "Kremlin agents".
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