ffmpeg is apparently outdated to do this. Get libav from its git:

Compiling from source
Make sure you have compilers installed:

apt-get update && apt-get install build-essential

Download latest libav from its Git:

git clone git://git.libav.org/libav.git

Download, compile and install yasm:

wget http://www.tortall.net/projects/yasm/releases/yasm-1.2.0.tar.gz
tar xf yasm-1.2.0.tar.gz
cd yasm-1.2.0
make && make install
cd ..

Download x264 codec and compile it:
git clone git://git.videolan.org/x264.git x264
cd x264
./configure –enable-static
make && make install

Now compile libav

cd libav
./configure --enable-gpl --enable-nonfree
make && make install

Update: The above compiles avconv without x264 support. When I tried to compile x264, I found a compile error.

Alternate method: Installation from repo:

apt-get install libav-tools
apt-get install libavcodec-extra-53
apt-get install libx264-dev
Convert a .wmv file to .avi on the linux command line

Converting wmv to mp4:

avconv -i 'myvid.wmv' -f mp4 -acodec mp2 'myvid.mp4'

Another command:

avconv -i myfile.wmv -strict experimental myfile.mp4


avconv -i myfile.wmv -c:v libx264 -c:a copy 'myvid.mp4'