"Servicemen and employees of Ukraine's armed forces... have called on the commander-in-chief to take urgent steps within the limits of existing legislation with a view to stabilising the situation in the country and reaching consent in society," the defence ministry said in a statement.
Yanukovych is the commander-in-chief of the Ukrainian armed forces.
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They "noted that a further escalation of the confrontation threatens the country's territorial integrity," the statement added.
Since November, Yanukovych has battled protests against his sudden decision to scrap a key pact with the European Union under the pressure from Russia.
These have since spiralled into an uprising seeking the president's removal.
Turmoil in Ukraine has shown no signs of abating and Yanukovych yesterday took indefinite sick leave after savaging the "irresponsible" opposition for inflaming tensions.
In a rare show of contrition, Yanukovych also admitted mistakes yesterday, promising to show "more understanding for the demands and ambitions of people".
The opposition and their supporters in the streets have refused to budge however, with leaders of the protest movement including boxer-turned-politician Vitali Klitschko preparing to meet top EU and US officials in Germany this weekend.
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