"No-one should expect that relations will suddenly deteriorate completely because of this decision," Binali Yildirim said.
Turkey recalled its envoy to Germany in protest against the resolution passed by German MPs on Thursday.
It promised to take "necessary steps".
Armenians say up to 1.5 million of their people died in the atrocities committed by Ottoman Turks in 1915, during World War One.
Turkey says the toll was much lower and rejects the term "genocide".
More than 20 countries, including France and Russia, recognise the 1915 massacre as "genocide", as do most non-Turkish scholars of the period.
Q&A: Armenian genocide dispute
Armenian 'genocide' vote ignites press
The Bundestag [German lower house] vote heightens German-Turkish tensions at a time when Turkey's help is needed to control migrant arrivals.
The resolution - adopted overwhelmingly - uses the word "genocide" in the headline and text. It also says Germany, at the time an ally of the Ottomans, bears some guilt for doing nothing to stop the killings.
The condemnation by Turkish politicians was widespread, including a joint statement by the ruling AK Party and two opposition parties which spoke of "indignation in the Turkish nation".
However, Mr Yildirim stressed that "Germany and Turkey are two very important allies". An estimated three million people of Turkish origin live in Germany.
The Turkish President, Recep Tayyip Erdogan, said the resolution would seriously affect relations with Germany, and that the government would consider further measures in response to the vote.
In a clear reference to Germany's Nazi past, Turkey's Foreign Minister Mevlut Cavusoglu tweeted: "The way to close the dark pages in your own history is not by besmirching the history of other countries with irresponsible and groundless parliamentary decisions."
But German Chancellor Angela Merkel said: "There is a lot that binds Germany to Turkey and even if we have a difference of opinion on an individual matter, the breadth of our links, our friendship, our strategic ties, is great."
Armenian tragedy still raw in Turkey
Turkey's prime minister has condemned as a "historic error" Germany's vote to recognise the 1915 massacre of Armenians as genocide, but said it will not wreck the two countries' ties.