On Sunday, Germany offered Poland several batteries from its Patriot missile defence system after two Poles died when a missile, believed to be Ukrainian, landed in Poland near the Ukrainian border.
But Poland has responded by suggesting Germany give the system to Ukraine.
"From a military point of view it would be best to place the Patriot batteries in Ukraine, at a certain distance from the Polish border," said Duda.
He added that this would allow the system "to protect Poland and its citizens as well as part of Ukraine," but noted that final decisions in the matter lay with Germany.
"If Germany does not agree that the system could be installed in Ukraine, then Poland should accept it," Duda wrote on Twitter.
According to Duda, Patriot batteries could be sent to Ukraine without Nato troops operating the system.
"Ukraine has been long asking for them and will surely agree that the batteries will be placed in such a location which will make it possible to protect also Nato states, for instance, Poland," the president wrote later in the day.
The German government has said that Nato restrictions mean that missiles cannot be located outside the alliance.
On Friday, Nato Secretary General Jens Stoltenberg said decisions on the Patriots' possible deployment in Ukraine were to be taken at the national level. (PAP)