Mr Medvedev, quoted by Russian news agencies, suggested that Western countries that accepted Ukraine's new authorities were mistaken. "The legitimacy of a whole number of organs of power that function there raises great doubts," he said. "Some of our foreign, Western partners think otherwise. This is some kind of aberration of perception when people call legitimate what is essentially the result of an armed mutiny. "He added: "We do not understand what is going on there. There is a real threat to our interests and to the lives of our citizens."
Ukraine's foreign ministry quickly responded to Mr Medvedev's comments on Russian citizens in the Ukraine, saying his concerns were "unfounded". However, Russia's foreign ministry also issued a strongly worded statement saying a "forced change of power" was taking place in Ukraine and accused interim leaders of passing new laws "aimed at infringing the humanitarian rights of Russians and other ethnic minorities".
Mr Medvedev's statement should not come as a surprise. It fits well with the Kremlin's policy of playing on Russians' nostalgia over the Soviet past and treating the West as bent on undermining the new, successful and powerful Russia.
With Ukraine out of the zone of Moscow's influence, President Putin's idea of a customs union which would bring the former Soviet republics under Russia's leadership, becomes a distant and doubtful dream.
"Defending the rights of Russians in Ukraine" is another political concept used by Moscow to promote its geo-strategic interests. The new authorities in Kiev will have to make sure that Ukraine's Russians do not feel excluded from the political process.
The concept had been used as a pretext in 2008 during the armed conflict with Georgia. Russia is now in control of its two breakaway provinces - South Ossetia and Abkhazia. Could the same happen in Crimea? Russia could support separatist sentiments in the region. However, most experts believe that Ukraine's territorial integrity is not in danger.
On Sunday, Ukraine's parliament reduced the official status of the Russian language by cancelling a law brought in by Mr Yanukovych. Meanwhile, EU foreign affairs chief Catherine Ashton has been in Kiev to discuss financial and political support for Ukraine's new leaders. Ukraine is facing bankruptcy and a promised loan from Russia is looking increasingly unlikely. She visited Independence Square - the scene of deadly clashes between protesters and police - and held talks with Interim President Olexander Turchynov.
Also on Monday, French President Francois Hollande called his Russian counterpart Vladimir Putin to urge a peaceful transition in Ukraine. A statement from Mr Hollande's office said he also emphasized "the importance of ensuring the unity and territorial integrity of the country". President Obama and German Chancellor Angela Merkel have also delivered similar messages to Mr Putin in recent days. On Monday, the US said it was ready to give financial support to Ukraine to complement any future loan from the International Monetary Fund .
Interim Interior Minister Arsen Avakov said on Facebook that a criminal case had been opened against Mr Yanukovych and other officials over "mass murder of peaceful citizens". He said Mr Yanukovych was last seen in Balaklava on the Crimean peninsula on Sunday. The peninsula is an autonomous region where the majority of the population is ethnically Russian. Crimea and some pro-Russian areas in the east have seen protests against the overthrow of Mr Yanukovych, sparking fears that Ukraine could be split apart by separatist movements.
Ukraine's political leaders aim to form a new unity government by Tuesday. Former PM Yulia Tymoshenko, who was released from jail on Saturday, has ruled out becoming prime minister. Her Fatherland party says she has accepted an offer of medical treatment in Germany. Ukraine's health ministry says 88 people, mostly anti-Yanukovych protesters but also police, are now known to have been killed in last week's clashes.
Thousands of people remain in Kiev's Independence Square, the Maidan.
Who is running Ukraine?
- Olexandr Turchynov - deputy leader of the Fatherland party and a long-time opponent of Mr Yanukovych; appointed interim president
- Arsen Avakov - also a key Fatherland MP, now interim interior minister
- Arseniy Yatsenyuk - parliamentary leader of Fatherland and the main negotiator during Maidan protests; tipped as a possible future prime minister
- Vitali Klitschko - boxer turned politician who was a leading figure in the Maidan; heads Ukrainian Democratic Alliance for Reforms (Udar); expected to run for presidency
- Oleh Tyahnybok - leader of far-right Svoboda (Freedom) party; key Maidan protest leader
- Yulia Tymoshenko - former prime minister and opponent of Mr Yanukovych; released from jail as opposition took control of parliament; has ruled out running for PM