In a statement after meeting Austrian Chancellor Werner Faymann, Cameron also suggested that the 28-nation bloc needed to increase its economic competiveness and give more sovereignty to EU members.
Britain plans to hold a referendum within two years on continued EU membership and is pushing for reforms within the bloc that reduce the authority of institutions at EU headquarters in Brussels.
Austria is a supporter of an EU with strong central authority, but like other nations, views Britain as an important member of the union and is prepared to compromise on some issues dear to London to keep it within the bloc.
The two countries share views on other issues, however. In the wake of the Paris attacks a week ago, Cameron called for a "stronger external EU border to protect our security with more effective screening and greater sharing of data between member states."
While Austria is struggling to deal with the refugee influx, Britain has applied strict restrictions on would-be asylum seekers.
But Cameron said both agreed for the need to a "comprehensive approach which tackles the (refugee) problem at source and stops migrants from making the perilous journey to Europe." That, he said, means more work with Turkey which hosts more Syrian refugees than any other country.
Cameron in Austria: Brits `not happy` with EU status quo
27 November 2015
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British Prime Minister David Cameron said Thursday that his fellow citizens are "not happy" with the EU status quo, the relationship between countries using the euro and those
