Another option, without needing the function
update points set country = t1.country from
select points.oid, countries.name as country from
countries INNER JOIN points on st_contains(countries.wkb_geometry,points.wkb_geometry)
where t1.oid = points.oid
I suspect (although I haven't tested) that this will be faster than using a nested function like in your example.
My output from running explain (hopefully your looks similar). If you have got more Seq Scan results, then that is something to look at, perhaps the indexes aren't quite set up properly.
Update on points (cost=1.18..29.40 rows=121 width=129)"
-> Nested Loop (cost=1.18..29.40 rows=121 width=129)"
Join Filter: _st_contains(countries.geometry, public.points.geometry)"
-> Hash Join (cost=1.18..2.37 rows=28 width=220)"
Hash Cond: (public.points.oid = public.points.oid)"
-> Seq Scan on points (cost=0.00..1.08 rows=28 width=114)"
-> Hash (cost=1.08..1.08 rows=28 width=110)"
-> Seq Scan on points (cost=0.00..1.08 rows=28 width=110)"
-> Index Scan using "countries_Idx" on countries (cost=0.00..0.91 rows=1 width=414)"
Index Cond: (geometry && public.points.geometry)"