The separatist Donetsk People's Republic also announced the ceasefire.
But an apparent violation was reported less than 90 minutes after the ceasefire began when Ukraine's Anti-Terrorist Operation Command reported that a military post near Zolote in the Luhansk region has been shelled by mortars.
As a positive sign, CNN reporters in Ukraine reported the shelling quieted shortly after midnight.
The peace agreement signed in Minsk, Belarus, several days ago comes with many questions over how it will be implemented and whether it will stick. Mistrust is high on both sides, adding to the doubts.
In his speech announcing the ceasefire, Poroshenko said Ukrainian troops control the town and warned militants to stay away.
"I think the fact of using the tense situation on the outskirts of Debaltseve by militants-terrorists-mercenaries poses a great threat, which can violate the ceasefire regime," Poroshenko said. "I am warning all participants of the Minsk negotiations, including the Russian Federation, which identifies itself as the guarantor of the reached agreements."
CNN's Nick Paton Walsh, reporting from the eastern town of Donetsk, said separatists claim to have encircled Debaltseve.
"Debaltseve will be a vital flashpoint for the hours ahead," he said.
Poroshenko has warned that if the separatists do not abide by the ceasefire, he will impose martial law throughout Ukraine's territory, his spokesman Andrey Zhigulin told CNN.
Poroshenko's office said he spoke on the phone with German Chancellor Angela Merkel, French President Francois Hollande and U.S. President Barack Obama in the hours before the ceasefire was due to take effect.
"The Ukrainian President has emphasized the need for monitoring by [Organization for Security and Cooperation in Europe] to confirm the ceasefire," a statement from Poroshenko's office said. "Petro Poroshenko and Barack Obama have agreed on further coordination of efforts in case of escalation of the conflict."
The White House said in a statement, "The President spoke with Ukrainian President Poroshenko today to express his sympathy for the mounting toll of the conflict in eastern Ukraine and his deep concern about the ongoing violence, particularly in and around Debaltseve."
Quiet after ferocious shelling
Separatist militants who spoke to CNN voiced their anger against government forces, whom they blame for the deaths and devastation in their communities.
Shelling rocked two eastern Ukrainian cities Saturday ahead of the ceasefire, raising fears that the deal to end a bitter 10-month conflict may be in jeopardy.
Both incoming and outgoing artillery could be seen in the vicinity of the coastal city of Mariupol, and there was significant shelling in Donetsk city, CNN teams reported.
Ukraine's National Defense and Security Council reported seven soldiers killed and 23 wounded in 24 hours. The council said additional forces were crossing the border from Russia into Ukraine in the area of Novoazovsk.
Igor Martinov, separatist-appointed mayor of Donetsk, said two people were killed and four injured by shelling in the city center Saturday afternoon. Photographs of the scene appeared to show one of the dead in camouflage gear and the other in civilian clothing.
Poroshenko said that after the agreement reached Thursday by the leaders of Ukraine, Russia, Germany and France, the offensive by the separatists had intensified.
The separatists may be trying to take control of strategic locations, such as the railroad hub of Debaltseve to the north, before the ceasefire lines are drawn. Pro-Kiev militia have also been pushing forward around government-controlled Mariupol.
As the shells rain down, the toll on eastern Ukraine's residents only grows.
The Ukrainian military operation against the separatists said Friday that 14 civilians had been killed by rebel shelling, six in the village of Shchastya, five in the village of Hornyak and three in Artemivsk, according to the official Ukrinform news agency.
Each side has accused the other of shelling civilian areas in the course of a conflict that has killed more than 5,000 people.
OSCE urges reduction of hostilities
Both sides are expected to start pulling back their heavy weapons from the front lines Monday, creating a buffer zone at least 50 kilometers (31 miles) wide.
The Organization for Security and Co-operation in Europe, which already has a monitoring mission in Ukraine
, has been given the challenging task of overseeing the process.
"We need to have an effective ceasefire," OSCE Secretary General Lamberto Zannier said Friday. "So I'm already concerned that we are seeing this morning a continuation of hostilities."
The OSCE hopes to see a reduction in hostilities between now and Saturday night, he said.
"I would expect the ceasefire to stop (armed) operations and to stop people where they are," he said.
While Ukrainian forces have to pull back their heavy weapons from the front line as they stood Saturday night, separatist forces must pull back theirs from the front line as it was on September 19, when a previous peace agreement was signed in Minsk. That swiftly disintegrated amid continued violence.
It also envisions prisoner swaps, new local elections in the conflict-affected regions of Luhansk and Donetsk, and a law granting amnesty to those involved in the the fighting.
However, Svyatoslav Tsegolko, a spokesman for the Ukrainian president, said that those responsible for shooting down Malaysia Airlines Flight 17 over Ukraine last summer will not be given an amnesty under the Minsk agreement.
This could be a potential hurdle to keeping the separatists on board.
Western governments believe rebels used a Russian-supplied missile system to shoot down the jet, having mistaken it for a military aircraft, while Kiev says it was a Russian officer who pressed the button. The separatists and Russia have denied any responsibility.
U.S. envoy: Separatists have more arms than some NATO states
The Kremlin has said it hopes to see the latest peace plan succeed.
But Kremlin spokesman Dmitry Peskov told Russia's state-run RIA Novosti on Friday that while Russia had helped to bring about the Minsk agreement, it wasn't in its power to fulfill it "because Russia is not a participant in the conflict."
Russia has steadfastly denied accusations by Kiev and the West that it is sending forces and heavy weapons into Ukraine.
But Kiev has accused it of continuing to do so even since the peace plan was signed in Minsk.
Geoffrey Pyatt, the U.S. ambassador to Ukraine, tweeted that the separatists "now have larger fighting force with more tanks armored vehicles, heavy artillery & rocket systems than some NATO and European countries."
He also posted satellite images which he claimed show "Russian military, not separatist, systems" deployed in eastern Ukraine.
The United States has not ruled out providing "lethal defensive aid" to the Ukrainian military to help it defend against advances by the Russian-backed separatists.
Ukrainian forces have just received a delivery of lightly armored military vehicles from Britain, but that country's Ministry of Defence said the vehicles were delivered as part of a commercial contract signed by a private company in 2013, before the conflict started.
A defense spokeswoman said Britain was not providing lethal aid to Ukraine. The trucks in question can offer protection to military personnel on the move but are not close combat vehicles, she added.