"In the first half of 2018 there were 1,500 requests for processing by Germany, and they will be accepted," Dimitris Vitsas told reporters.
Berlin and Athens signed a deal at a recent EU migrant summit aimed at stemming arrivals to Germany and Austria - with some asylum seekers likely to be returned to the first EU country they reached, often southern Mediterranean states such as Greece and Spain.
Vitsas said the deal sought "to find a uniquely European solution to regulate the migrant influx and limit unilateral actions."
German Chancellor Angela Merkel has marketed the Greek accord and another with Spain as a way to placate hardline rebels within her government.
In return for processing the asylum applications of migrants who reached Germany, Berlin has promised to accept 2,900 migrants from Greece for family reunification, Vitsas said.
The minister said that arrivals from Turkey had fallen by 96 percent since their peak in the summer of 2015, but Greece is still struggling to look after some 60,000 migrants already on its territory.
He said Greece was dealing with "problems with integration and housing" for migrants, especially in overcrowded camps on the Dodecanese islands, just a short boat ride from Turkey.
The International Organization for Migration says more than 50,000 migrants and asylum seekers have reached Europe by boat since the start of 2018, with more than 1,400 dying en route.