It comes as Germany's leader condemns days of violent protests against refugees and migrants.
The diplomatic push was made during talks between German Chancellor Angela Merkel and French President Francois Hollande in Berlin.
Ms Merkel says the EU's laws about registering migrants are not being followed by some countries.
"We have joint asylum rules in Europe, but those rules are currently not implemented and Germany and France expect that all member states fully implement these asylum rules. We're talking specifically about the registration of migrants, about minimum standards of accommodation and minimum standards of health care."
France's President, Francois Hollande, has also called for an equal distribution of refugees across the EU.
"The Chancellor has referred to those measures which we are proposing. First of all, that there should be an acceleration of the establishment of reception centres in Italy and in Greece. This is indispensable for registering people who come to our shores to enter Europe and to make at this point the necessary distinction between the people who are claiming asylum and the people who are coming here simply to migrate."
Europe has been struggling with a massive influx of people fleeing conflict, persecution and poverty.
Migration officials say a record 107,000 people arrived at Europe's borders last month.
Most arrive in Greece - which is dealing with its own economic crisis - and Italy.
After being processed in Greece, the migrants usually make their way across the border to the Former Yugoslav Republic of Macedonia.
From there, they set off on foot to Serbia before heading north for Hungary from where they hope to enter EU countries.
But Austria's Foreign Minister, Sebastian Kurz, has told Al Jazeera Greece is responsible for the flood of migrants.
"It's also the fault of Greece, if there is no support for the refugees there."
EU Foreign Policy chief Frederica Mogherini says assigning blame isn't helpful.
"I think in this story of this huge migration flow and refugees flow that we are experiencing due to the large number of crises we have around us, we have to realise that the blame game is not bringing any kind of positive result for any of us. The main point is not saying who is doing his homework or not. The point is how do we face together the challenge and how do we manage together the issue?"
Apart from the strain the migrant influx is placing on many countries in Europe, tensions are also being heightened.
Violent protests against refugees have already taken place in the east of Germany.
Angela Merkel has condemned clashes over two nights between police and far-right protesters opposing the opening of a new centre for refugees.
"I'd like to say, after the horrifying images from Heidenau and Saxony, that I strongly condemn the violence there. And the atmosphere of racism we saw is not at all acceptable. It's repulsive to see how right-wing extremists and neo-Nazis are voicing their hatred. But it's just as disgraceful to see how German citizens and even families with children are supporting this by marching along with them."
Politicians in Germany are warning of an increase in hostility towards foreigners.
In the first half of the year alone, some 150 arson or other attacks were carried out on refugee shelters.
Germany takes in the largest number of refugees in Europe and expects up to 800,000 people will have sought asylum by the end this year.
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