"These criminal acts of the enemies of the Ukrainian people will not go unpunished," he was quoted as saying by the Unian news agency.
The helicopter was shot down near the eastern city of Slavyansk.
An army general was among those killed.
Slavyansk has seen fierce fighting between the rebels and Ukraine's army.
Russia has reiterated calls for Ukraine to stop its military campaign against the pro-Moscow rebels and "start a real national dialogue".
In a separate development, Ukraine, Russia and the EU are due to open a new round of talks in Berlin on resolving a growing dispute over Moscow's gas supplies to Kiev.
Russia's Gazprom has threatened to cut off gas supplies to Ukraine if it fails to pay its huge debt.
At the scene reporting
The helicopter arrived at Karachun, near Slavyansk , to unload and pick up a group of people who were finishing their tour and going on leave.'Criminals destroyed'
They were shot down after take-off.
I had talked to the pilot and also to Maj Gen Serhiy Kulchytskiy.
The pilots were very nice guys - polite, correct, friendly.
Gen Kulchytskiy was very capable and very accessible, a good commander who would fly to the checkpoints where his soldiers were.
He would personally bring them food and water.
He kept an eye on everything.
The fighting here has become more frequent recently.
In the last few days, it broke out even during the daytime.
Previously, it happened only at night.
However, the last two days were relatively quiet.
The army man checkpoints, preventing the forces of the People's Republic of Donetsk from moving about freely.
The mood is good among the soldiers.
No desertion or talk about giving up.
People are in good fighting spirit.
Mr Poroshenko, who won last Sunday's presidential elections, expressed his condolences to the families of the helicopter crew.
"We must make every effort to make sure that no more Ukrainians die at the hands of terrorists and bandits," he said.
The Mi-8 helicopter was hit during heavy fighting between Slavyansk and Kramatorsk, Donetsk region, after it had dropped off troops at a military base.
The 14 people on board were killed, including Maj Gen Kulchytskiy, head of combat and special training, the Ukrainian National Guard said.
It added that the "criminals" who attacked the helicopter were later "destroyed" by Ukrainian troops involved in an "anti-terror" operation.
Two helicopters were also shot down by separatists earlier this month.
The conflict has intensified in recent days.
The rebels say they lost up to 100 fighters when they unsuccessfully tried to seize Donetsk's international airport on Monday.
Among those killed were 33 Russian nationals, a separatist leader said.
US Secretary of State John Kerry said there was also "evidence of Russians crossing over, trained personnel from Chechnya trained in Russia, who've come across to stir things up, to engage in fighting".
Chechnya's president has denied sending troops to Ukraine.
Pro-Russian separatists in the regions of Donetsk and Luhansk declared independence after referendums on 11 May, which were not recognised by Kiev or its Western allies.
The rebels took their cue from a disputed referendum in Crimea, which led to Russia's annexation of Ukraine's southern peninsula.
Ukraine's deadliest clashes
- 24 April: Ukraine military kills five rebels in assault on Slavyansk
- 2 May: More than 40 people killed in burning building after street fighting in Odessa
- 9 May: 20 pro-Russian activists and Ukrainian security officer killed in Mariupol
- 13 May: Seven Ukrainian soldiers killed in ambush between Slavyansk and Kramatorsk
- 22 May: Rebel attack on checkpoint in Volnovakha leaves at least 14 soldiers dead
- 27 May: At least 50 rebels killed (rebels claim 100 killed) in "anti-terrorist operation" against separatists holding Donetsk airport
- 29 May: Ukrainian military helicopter shot down near Slavyansk, killing 14