Berlin would "send Patriot anti-aircraft systems to Poland and support the securing of Polish airspace with Eurofighter (jets)", Defence Minister Christine Lambrecht said in a statement.

Two people were killed last week when a missile landed in the Polish village of Przewodow, six kilometres (four miles) from the Ukrainian border.

Warsaw and NATO have said the explosion was likely caused by a Ukrainian air-defence missile launched to intercept a Russian barrage, but that Moscow was ultimately to blame because it started the conflict.

Before the deal was agreed, Polish Defence Minister Mariusz Blaszczak said he "welcomed the German proposal with satisfaction".

Blaszczak said on Twitter he would propose for the systems to be "stationed close to the border with Ukraine".

Germany has already sent Patriot anti-aircraft units to Slovakia, where Berlin hopes to keep them deployed for longer than currently planned.

The air-defence systems should remain in Slovakia "until the end of 2023 and potentially even beyond", Lambrecht told the Rheinische Post daily.

"It is our utmost responsibility that NATO does not become a participant in this conflict," while strengthening its air defences, she said.