Cameron, who chaired a meeting of British military and security chiefs in London to discuss the crisis, said the world needed to send a "clear message" to Moscow.
He said: "What we want to see is a de-escalation rather than a continuation down the path that the Russian government has taken, violating the sovereignty and territorial integrity of another country.
"So we shall have to bring to bear diplomatic, political, economic and other pressures in order to make this point.
Cameron was speaking after Ukraine's military said Russia had issued an ultimatum to Ukrainian forces to surrender in the Crimea or face an all-out assault on the Black Sea peninsula.
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The Russian Black Sea fleet dismissed the claims as "nonsense", but Cameron said the reports were "deeply concerning", adding that "we all want to see stability and countries obeying the rule of law".
British Foreign Secretary William Hague warned Russia today of "consequences and costs" as he met Ukraine's new Western-backed leaders in Kiev.
"It is not an acceptable way to behave and there will be consequences and costs," he added.