"If the current trend continues then we will reach a total of between 90,000 and 100,000 deportations and voluntary returns," de Maiziere told reporters.
"That is good but not good enough. That is why we must continue to work to ensure that those who must leave our country actually do so."
Between January and April of this year, some 20,000 foreign nationals without permission to stay in Germany returned to their countries of origin voluntarily under government programmes.
Those totals marked a strong increase from 2015, when 37,220 returns were recorded during the year as a whole, and 13,574 in 2014.
German authorities said 9,280 were deported during the first four months of 2016, compared to 22,369 in all of 2015 and 13,851 in 2014.
De Maiziere did not provide a breakdown of the migrants' countries of origin.
Germany has said it aims to speed up the returns of people not granted asylum after the arrival of nearly 1.1 million people fleeing war and poverty in 2015.
In particular it has aimed to streamline processing of asylum applications and classified several Balkan states as safe countries of origin to accelerate expulsions. It has also moved to place certain North African countries on the same list.
Germany recorded a steep decline in asylum-seeker arrivals in April, according to official data last month, after the closure of the popular route used by migrants through the Balkans.
Some 16,000 migrants arrived in April, down almost a quarter from 20,000 in March, and nearly a 90-percent plunge from December when 120,000 arrivals were recorded.