"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

Mark Yeates twice threatened for Blackpool before the break, with his second effort tipped onto the bar.
A fine run from Stephen Darby set Reid up to fire low into the bottom corner.
Blackpool's Will Aimson saw red in injury time for a second caution after a clash with James Henson.
Defeat sees Blackpool slip to within one spot of the relegation places, with the Seasiders only above Shrewsbury in 21st on goal difference.

The initiative at The Meadows, along the Melville Drive side, comes ahead of a wildlife meadow being planted.
At least 10 large tree logs have been installed by the City of Edinburgh Council after Friends of the Meadows and Bruntsfield requested them.
The logs have been donated by the forestry service.
Lesley Hinds, City of Edinburgh Council's environment convener, said: "We have been working closely with Friends of the Meadows and Bruntsfield Links over recent months to install these logs, which will not only deter drivers from parking along the edge of the Meadows, but will help our efforts to encourage and diversify wildlife in the area, along with a new wildflower meadow."
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.
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Kyel Reid scored the only goal of the game as Bradford City moved to within a point of the play-off spots with victory over relegation-threatened Blackpool at Bloomfield Road.
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Logs have been embedded into the grass at a huge city park in Edinburgh in a bid to encourage insects and other wildlife to the area.