In a letter from prison, written in response to questions from CNN, she said: "If Putin wants to defeat Ukraine -- let's try to defeat me first!"
"But if he wants peace and friendship between our nations as he claims," she added, "I am ready to make the first step towards it.
"My freedom will be that first step towards peace and understanding in Ukraine."
Savchenko has been held by the Russian authorities in pre-trial detention since last June. Her defiant message was written after CNN submitted a series of questions to the Ukrainian fighter pilot through one of her lawyers, Mark Feygin. We do not know under what circumstances Savchenko answered the questions, but Feygin says she wrote the responses on Friday as he was visiting her.
Savchenko undertook a hunger strike for 83 days to protest her detention despite pleas from her family and her lawyers. She recently abandoned her fast after nearing death but has since resumed it, only drinking broth and milk occasionally to stay alive.
Russia claims the 33-year-old is behind the killings of two Russian journalists hit by mortar fire at a checkpoint in eastern Ukraine, allegations she has always denied. Moscow says she then crossed voluntarily into Russia and sought asylum as a refugee. The Ukrainian government, however, insists she was kidnapped by rebel forces and that she is a prisoner of war.
"I have already been in captivity for an hour when those Russian journalists died. I have not seen them, and our ways have never crossed.. The 'rebels' themselves told me that those journalists came under fire of their own 'makhnovtsi' [slang for 'anarchists']," Savchenko told CNN in her letter from jail.
"And the investigators knew all about it since the very beginning! And they have nothing on me! They simply thought that it would be easy to "twist my arms" and receive another star for their epaulettes. But it's not going to happen!" she added.
Savchenko's case has attracted wide international attention and turned her into a symbol of resistance against Russia in her home country, with Ukraine's President Petro Poroshenko awarding her the title "Hero of Ukraine," one of the nation's highest honors. She has also been voted into the Ukrainian parliament despite her captivity.
Despite her critical situation, Savchenko appears to have retained her sense of humor just as much as her determination, writing that she was feeling "On the edge!...;) Close to Nirvana and enlightenment!;) Joking."
"Holding on! But holding my body entirely on my the power of my will," she continued, "because I am so numb that I couldn't feel the needle when the blood sample was taken from my vein today.
"Tottering, head is spinning, [blood] pressure 80x40, [blood] sugar 2.9, T [temperature] -- 35.7°C. But still be standing till 50kg [body weight]! Even longer if God let's me! Hasn't fainted even once and hasn't fallen off my feet."
The military pilot told CNN she is being monitored "24 hours a day," which she finds "very annoying."
"Protection and security measures are such that King Kong would not have been able to break away!;)," she joked again.
"But in general all is very decent and polite! Treatment is reasonable."
Savchenko's lawyer recently told CNN's Christiane Amanpour in an interview that President Putin holds Savchenko's fate and that she wanted to await trial out of jail.
Several international dignitaries have urged Moscow to release her, including EU Foreign Policy Chief Federica Mogherini and the U.S. State Department, to no avail.
But as Savchenko continues her hunger strike, is she willing to ultimately die in detention?
"To die?! That's not our methods!!!;) I'll think of something better!...:;)," she said.
"I'll be on hunger strike as I said until I am returned back to Ukraine, or at least [until] detention is changed to a house arrest at the Ukrainian Consulate in RF, which is actually a part of Ukraine in Russia.
"There is no point starting eating in prison. The bite doesn't go down the throat here in this cage! And the truth must win after all!!!"
CNN reached out to Russian authorities for an update on Savchenko's case, who referred us to their last statement on Savchenko, dated from 20 February, where they call on the media to "Let the investigators to finish their job. Let the court of justice to determine Savchenko's degree of guilt of and punishment for the crimes she is charged with."
Savchenko is currently scheduled to appear in court on May 13.