"We can't afford this in the world. That's why if the instruments of diplomacy won't work, if all negotiation instruments won't work and personal relations with Mr Putin won't work, the world has to apply strongest means."
Ms Amanpour replied: "You sound like you're raising the stakes and you are calling for the West, the United States, Britain, Europe, to use military force against Russia. Am I reading you correctly? Is that what you are calling for?"
Tymoshenko responded: "I am asking all the world, personally every world leader, to use all the possibilities in order to avoid Ukraine losing Crimea."
She also claimed the Russian Duma has started listening to a draft law to annex Crimea from Ukraine.
The 53-year-old added: "It's only a question of time when it (will) be voted. We all know that votes in Duma will be found.
"That's why Russia is escalating the crisis now. And the world should understand, should realise, that Ukraine on its own won't be able to solve this issue with Russia on its own. Absolutely not possible."
Her comments come as Ukrainian Defense Ministry spokesman Maksim Prauta said Russian forces controlling the strategic region of Crimea demanded the crew of two Ukrainian warships surrender.
It was alleged they then demanded all Crimean troops withdraw by 3am - or face action.
Moscow swiftly denied they had made the ultimatums - and accused Ukraine of trying to spark war by making the claims.
The news comes as top EU official says the bloc's 28 leaders will hold an emergency summit on Ukraine Thursday. They are expected to freeze visa liberalization and economic cooperation talks with Russia if Moscow hasn't taken steps to calm the crisis.
It called on Russia on Monday to withdraw its troops to bases and hold consultations with Kiev, while extending the possibility of holding a summit of EU leaders to discuss the crisis in Ukraine.
World leaders continued to condemn action in the region.
President Barack Obama said Russia is "on the wrong side of history" in Ukraine and its actions violate international law.
Obama told reporters in the Oval Office on Monday that the United States is considering economic and diplomatic options that will isolate Russia. The president called on Congress to work on an aid package to Ukraine and make it the 'first order of business.'
Obama said continued military actions in Ukraine "will be a costly proposition for Russia".
"And now is the time for them to consider whether they can serve their interests in a way that resorts to diplomacy as opposed to force," he added.
- Daily Mail