There has been a surge in fighting between Ukraine government forces and pro-Russian separatists in recent days.
On Saturday, at least 30 civilians were killed in shelling in the southeastern city of Mariupol, while eight people died when a transit stop in the city of Donetsk was shelled Thursday.
Both sides blamed the other for the deaths.
Speaking after a meeting with the European Commissioner for Humanitarian Aid and Crisis Management, Poroshenko said "the actions of Russian-backed terrorists and regular Russian troops" had caused Ukrainians to suffer.
"We are going to file a suit to the Hague tribunal, which must investigate into these crimes against humanity," Poroshenko said.
"It is a test for humanity and moral dignity. Because turning a blind eye to such horrible and shameful crimes means indulging terrorists and aggressors and violating high European values for which Ukrainians are suffering and dying."
On Sunday, Ukraine's National Security and Defense Council authorized the government to initiate the Hague action, it said in a statement.
It said it would ask for the Donetsk People's Republic and Luhansk People's Republic to be designated terrorist organizations.
The International Criminal Court at the Hague is a permanent body established by 120 nations to investigate "the most serious crimes of concern to the international community."
Earlier Monday, Moscow stepped up its war of words over Ukraine, warning Western countries not to give Kiev the impression it had their automatic support regardless of its actions.
At a press conference in Moscow, Russian Foreign Minister Sergey Lavrov blamed Kiev for the renewed fighting and civilian deaths and questioned the West's lack of condemnation.
Lavrov said Moscow -- which accuses Ukrainian forces of responsibility -- had not heard a single statement from the West criticizing Kiev.
"We hope our Western partners won't stay away, and European countries, primarily France and Germany who are taking part in so called Normandy format, and mainly the U.S. won't do anything to create an illusion for Kiev's government that its actions lead to automatic support in the West."
Lavrov said there was no other path to resolve Ukraine than direct dialogue between Ukraine's conflicting sides.
Fighting between Ukraine government forces and pro-Russian separatists broke out last spring, slowing for a short-lived ceasefire agreed to in Minsk, Belarus, in September.
Ukraine and the West accuse Russia of sending troops and equipment over the border to help the separatists, allegations that Russia denies.
The United States and European Union have imposed financial sanctions against Russian interests.
The U.S. State Department on Sunday said Secretary of State John Kerry and Lavrov had spoken by phone about the shelling of civilians.
"The secretary reiterated our condemnation of the separatists' grad missile attack on civilians in Mariupol yesterday 25 kilometers beyond the Minsk line, and other separatist attacks in blatant violation of the agreement.
"The secretary reiterated the need for an immediate resumption of the ceasefire, a withdrawal of heavy weapons, and closing the border. He also underscored U.S. readiness to participate in serious settlement efforts, making clear that de-escalation is in everyone's interests, that Russia will be judged by its actions, and that the costs to Russia will only increase if attacks continue," a representative said.
The White House says Vice President Biden also spoke with Ukrainian President Poroshenko on Saturday.
They "expressed grave concern over Russia's blatant disregard for its commitments under the September Minsk agreement and unilateral escalation of the conflict," the White House said.
The two leaders vowed to "ensure that the costs continue to rise on Russia for its aggressive actions against Ukraine."
"Those who give such criminal orders bear responsibility for this. People doing that should know that there is no other way of resolving such conflicts than peace negotiations and political measures," he said.
On Monday, the state-run Itar-Tass news agency reported Russian President Vladimir Putin as saying a "NATO legion" was working in Ukraine with the aim of containing Russia.
"In essence, this is already not an army, but a foreign legion, in this case NATO's foreign legion that certainly does not pursue the goal of defending Ukraine's national interests," Itar-Tass quoted Putin as saying.
But following a special session of NATO's Ukraine commission in Brussels, Belgium, Secretary General Jens Stoltenberg told journalists that Putin's allegations were "nonsense."
Stoltenberg said there was no NATO legion and "the only foreign forces in Ukraine are Russian."
The conflict in eastern Ukraine broke out last spring after Russia annexed Ukraine's southeastern Crimea region and as pro-Russia separatists claimed control of the Luhansk and Donetsk regions.
The ceasefire from Minsk crumbled long ago.
From mid-April to January 21, the conflict killed at least 5,086 people and injured at least 10,948 others, according to the United Nations.
"We fear that the real figure may be considerably higher," the Office of the U.N. High Commissioner for Human Rights said about the death toll in a report released Friday.