Morawiecki also accused Germany of shirking from the issue and stalling.
Defence Minister Mariusz Blaszczak said earlier on Tuesday that a request for consent had been sent to Berlin, which controls the vehicles' exports licences to non-Nato countries.
Asked at a press conference how long Warsaw would give Berlin to reply to the request, Morawiecki answered: "I hope that the response from the German side comes quickly this time, because the Germans are lingering, dodging, acting in a way that is difficult to understand."
The prime minister added that it was clear to see that Germany was unwilling to help defend Ukraine more broadly.
"What does this mean?" he asked. "Does it mean fear, some not-entirely-comprehensible dread, or faith that a return to normal relations with Russia is possible?" He went on to say that it was worth asking such questions as the coalition of states ready to aid Ukraine must grow.
Morawiecki pointed out that Germany is Europe's biggest economy and should contribute greatly to the coalition of countries aiding Ukraine.
"We expect a quick response," he said. "Of course we are already training Ukrainian soldiers in Poland; other countries are also doing that on their territories."
A German government spokesman was later quoted by the dpa news agency as confirming that Berlin had received the request, which would be "considered with the necessary urgency in line with established procedures and guidelines concerning the export of arms."
Later on Tuesday, Morawiecki said in an interview for the British broadcaster BBC News that Poland was going to wait for up to two weeks but was ready to transfer the tanks to Ukraine regardless of Berlin's answer.
Morawiecki said that Warsaw wanted to deal with the issue while observing all the required procedures and expressed hope that Germany will respond to Poland's request as quickly as possible.
Also on Tuesday, the Bloomberg news service reported that "Germany is expected to give Poland approval as soon as Wednesday," quoting "people familiar with the matter, who asked not to be identified." (PAP)