The EU described reports of the hunger strike as "extremely worrisome" and called for the immediate release of 34-year-old Nadiya Savchenko.
"Russia bears responsibility for the health, well-being and observance of the human rights of all persons it detains," an EU spokeswoman added.
Three Nobel Prize laureates are among thousands of people who have signed a petition urging European leaders "to take emergency measures" to seek Savchenko's return home.
The helicopter pilot is standing trial for alleged involvement in the 2014 death of two Russian journalists in war-scarred eastern Ukraine.
She faces up to 23 years in prison if convicted in a trial that has drawn global attention and been attended by Western monitors concerned about Russia's allegedly deteriorating record on human rights.
Savchenko denies the charges and has refused all food and drink since her hearing was adjourned on Thursday before she was given a chance to make a final statement.
Poroshenko wrote on Facebook that "Ukraine has sent a letter to EU nations and the United States with the request to intensify their pressure on Russia aimed at securing our Nadiya's release."
He added that Savchenko was also visited in her southern Russian detention centre on Monday by Ukraine's consul general.
Ukraine's Hromadske Radio's website afterwards posted a hand-written note that was signed by Savchenko and dated Monday.
"Whether dead or alive, I have already won," said the message.
"I will leave jail on my own terms, showing the entire world that Russia may be forced into submission if you remain as fearless and unyielding as me."
Savchenko's case is seen by many Ukrainians as a symbol of resistance against what Kiev's pro-Western leaders view as Russia's aggression in the eastern industrial heartland of the former Soviet state.
- 'Mockery of civil rights' -
Her fate has also sparked concern among Western governments and leading human rights groups.
The Belarussian writer Svetlana Alexievich and two other Nobel Prize winners in literature -- Austria's Elfriede Jelinek and the Lithuanian-American Tomas Venclova -- told European leaders that Savchenko's life and the bloc's credibility were at stake.
"Our ability to save her life will test the effectiveness of international diplomacy and our commitment to European values," said an open letter posted online Sunday and signed by more than 5,000 people.
"The Russian authorities have made a mockery of civil rights, international law, and their own Constitution."
US State Department spokesman John Kirby stressed on Thursday that Savchenko "needs to be released".
Prosecutors argue that Savchenko helped Ukrainian forces locate and direct mortar fire at two Russian state television journalists in the separatist region of Luhansk.
She counters that she was in the area of the attack incidentally and was kidnapped and smuggled into Russia.
Savchenko's supporters especially fear that her refusal to drink may irreparably damage her health or even kill her before her next hearing on Wednesday.
One of Savchenko's Russian attorneys said his client was already suffering from "an accelerated heart beat, swelling legs and jumps in temperature."
"She is still forbidding Russian doctors from performing any tests or medical procedures," lawyer Nikolai Polozov wrote on Facebook.
And her second attorney in the case said that while "her condition is more or less satisfactory, we are seeing the consequences of her hunger strike.
"She believes that the sooner these hearings are over, the sooner she can return to Ukraine," lawyer Mark Feygin told AFP.
"But that is not how these things work."
The separatist war in Ukraine has claimed more than 9,200 lives since pro-Russian insurgents angered by the ousting of Ukraine's Moscow-backed leadership revolted against the Kiev authorities in April 2014.
Russia rejects Ukrainian and Western charges of instigating and backing the unrest.