Poroshenko discussed reports of the incursion of armored personnel carriers from Russia with British Prime Minister David Cameron and said that a "considerable part of this equipment was destroyed overnight by Ukrainian artillery".
The latest incident has signalled the worsening of the country's conflict with pro-Russian separatists who took over parts of eastern Ukraine, as Kiev accuses Moscow's military of arming and backing the fighters.
Earlier on Friday, NATO secretary-general Anders Fogh Rasmussen confirmed witnessing the Russian "incursion" into Ukraine, which Russia denies, Al Jazeera reported.
During a visit to Denmark's capital Copenhagen, Fogh Rasmussen told reporters: "I can confirm that last night we saw an incursion (into) Ukraine."
Rasmussen did not give details of the alleged incursion but said "what we have seen last night is the continuation of what we have seen for some time".
Russia's federal security service said Russian forces are patrolling the border area but denied that military vehicles had moved into Ukraine.
Moscow has accused Kiev of attempting to disrupt a Russian humanitarian aid mission to eastern Ukraine and called for a ceasefire in the region to allow for the deliveries.
"We draw attention to the sharp intensification of military action by Ukrainian forces with the apparent aim to stop the path, agreed on with Kiev, of a humanitarian convoy across the Russia-Ukraine border," the Russian foreign ministry said in a statement.
Britain said it summoned Ambassador Alexander Yakovenko to clarify the reports of the Russian military invasion.
Earlier, Russia let Ukrainian officials inspect an aid convoy while it was still on Russian soil on Friday and agreed that the Red Cross can distribute the goods in Ukraine's rebel-held city of Luhansk. The twin moves aimed to dispel Ukrainian fears that the operation was a ruse to get military help to the pro-Russian separatists.