Since I had to do this task quite often, I summarize the necessary steps.
First get the data (in this case for the Eurasian block) from

ftp://e0srp01u.ecs.nasa.gov/srtm/version2/SRTM3/Eurasia/

E.g. I downloaded the area between N43-45/E141-144. Thereafter unzip and convert with GMT by

xyz2grd -V N44E141.hgt -R141/142/44/45 -GN44E141.grd -I0.05m -Zhw
xyz2grd -V N44E142.hgt -R142/143/44/45 -GN44E142.grd -I0.05m -Zhw
xyz2grd -V N44E143.hgt -R143/144/44/45 -GN44E143.grd -I0.05m -Zhw
xyz2grd -V N43E143.hgt -R143/144/43/44 -GN43E143.grd -I0.05m -Zhw
xyz2grd -V N43E142.hgt -R142/143/43/44 -GN43E142.grd -I0.05m -Zhw
xyz2grd -V N43E141.hgt -R141/142/43/44 -GN43E141.grd -I0.05m -Zhw

And after this, combine all 1×1 degree blocks to a huge 3×2 degree block

grdpaste N43E141.grd N43E142.grd -GA.grd
grdpaste A.grd N43E143.grd -Gl.grd
grdpaste N44E141.grd N44E142.grd -GA.grd
grdpaste A.grd N44E143.grd -Gu.grd
grdpaste l.grd u.grd -Gall.grd


Finished. Now all.grd covers the complete area.