Prosecutors are demanding a 23-year jail term for Savchenko's alleged involvement in the killing of two Russian state TV journalists in war-torn eastern Ukraine in 2014.
Few doubt that the 34-year-old combat helicopter navigator -- who denies the charges and says she was abducted and smuggled into Russia -- will be found guilty, and Kiev is already pushing for a prisoner swap.
The judge began by reading out the prosecution allegations that Savchenko acted as a "spotter" in the fatal shelling of journalists Igor Kornelyuk and Anton Voloshin in June 2014, just two months after the start of the pro-Kremlin uprising in Ukraine's industrial east.
At the time, she was serving in a volunteer pro-Kiev battalion fighting the insurgents.
Since her arrest, Savchenko has become a national hero in Ukraine and has even been elected to parliament in absentia.
Footage from the courtroom showed a relaxed-looking Savchenko chatting with her lawyers from inside the glass-fronted defendants' cage as the judge read out the ruling.
An AFP correspondent was barred from the courtroom in the southern Russian town of Donetsk and early reports from Russian new agencies appeared to indicate incorrectly that Savchenko had been handed a definitive guilty verdict.
The reading of the verdict is set to last through Tuesday.
"You heard the first introductory and explanatory parts, some media hurried with the guilty verdict," Savchenko's lawyer Mark Feigin told journalists during a break in proceedings.
"It will be guilty of course, you need not doubt that, there is no doubt and there will be a long sentence."
Hunger strikes
Another of Savchenko's lawyers, Nikolai Polozov, told journalists that his client would not appeal the court's decision as she considered it "has nothing to do with justice" and would start refusing water 10 days after the verdict.
Savchenko has repeatedly gone on hunger strike in protest at her trial and detention -- fasting for more than 80 days at one point and going almost a week without food and water at another.
Ukraine and its Western allies have condemned Savchenko's case as a political show trial and see it as part of the Kremlin's broader aggression against its ex-Soviet neighbour that saw Moscow seize the Crimea peninsula and fuel a separatist insurgency.
Ukraine's pro-Western President Petro Poroshenko has pledged to do "everything possible" to bring Savchenko back home and mooted a prisoner swap to free her.
Kiev is holding two men it says were Russian soldiers serving in the east of the country, who could provide Poroshenko with a possible bargaining chip.
But Moscow is also thought to have at least 10 other Ukrainians behind bars -- including well-known detainees like film director Oleg Sentsov -- and the Kremlin has given little hint it is ready to play ball.
Western pressure
Savchenko has struck a defiant figure throughout the long months of her detention, which saw her sent to a psychiatric hospital near Moscow before being transferred close to the Ukraine border for her trial in the town of Donetsk.
Usually dressed in a traditional Ukrainian blouse or pro-Kiev T-shirt, Savchenko has ridiculed the court from the defendant's cage and flashed her middle finger at the judges earlier this month as her trial ended.
Ties between Moscow and Kiev are already in tatters over the 2014 seizure of Crimea and the subsequent separatist insurgency in the east.
A complex political process to end the conflict in eastern Ukraine has stalled as Kiev and Moscow accuse each other of failing to live up to promises made in a peace deal signed over a year ago.
Russia has meanwhile thrust its way back to the centre of the international diplomacy with its air campaign in Syria, prompting some in Kiev to fear the West might ease the pressure over Ukraine.
A guilty verdict and harsh sentence for Savchenko could refocus Western attention, however, and Kiev is pushing for sanctions on some 40 people it says are "directly involved" in Savchenko's case.
Poroshenko's wife Maryna appealed to US first lady Michelle Obama in a letter to join the international campaign to secure the Savchenko's return and release, the Ukraine president's website said Monday.
Ukraine also protested after top lawmaker Iryna Gerashchenko said Russia's FSB security service stopped her from entering the country to attend the hearing.
