Frank-Juergen Weise told a newspaper that his office would struggle if more people came. But he said he was confident the number of new arrivals would remain within the estimate.
More than one million migrants from the Middle East, Afghanistan and Africa arrived in Germany last year. The German interior ministry says more than 390,000 people applied for asylum in the first six months of this year, but it is not clear how many of these may have arrived in the country in 2015.
Weise said Germany would try to get as many of them on the job market as possible. But he said the migrants' integration in German society "would take a long time and cost a lot.
Around 15 protesters spent nearly an hour on top of the Brandenburg Gate on Saturday, with banners calling for "secure borders, secure future. A poll this month showed just over half of Germans thought Chancellor Angela Merkel's migrant policy was bad.