Berlin had already agreed in March to take in some 5,000 Syrian refugees needing "special protection", giving them an initial permit for a two-year stay and settling them all around the country.
Now with the additional number, Germany appears prepared to accept a total of 10,000 Syrian refugees, according to news agency DPA, citing a minister at the meeting who confirmed a report in the Welt newspaper.
According to the paper, the decision was a compromise between the request of the left-wing Social Democrats for 20,000 refugees and the conservatives.
In September, Germany welcomed the first wave of Syrian refugees which were part of the contingent approved in March.
More than 18,000 asylum requests from Syrians have been granted by Germany since 2011, when Syria's conflict started, government spokesman Steffen Seibert said at the time.