He told Germany's Bild newspaper he hoped the ships could be relocated "to assist Ukraine and provide security".
On Sunday, Russia opened fire on three Ukrainian ships and seized their crews in the Kerch Strait between the Black Sea and the Sea of Azov.
Nato has expressed "full support" for Ukraine, which is not a member state.
Amid worsening relations on Wednesday, Russian President Vladimir Putin accused Mr Poroshenko of creating the naval "provocation" to boost his ratings ahead of 2019 elections.
President Poroshenko has implemented martial law across Ukraine's border regions for 30 days in response to the crisis.
What did Poroshenko say?
In the interview with Bild, Mr Poroshenko said Vladimir Putin wanted "nothing less than to occupy the [Azov] sea".
"Germany is one of our closest allies and we hope that states within Nato are now ready to relocate naval ships to the Sea of Azov in order to assist Ukraine and provide security," he said.
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