How to use MinGW-w64 with Cygwin?

MinGW-w64 has been available with Cygwin at least since December 2010. However I am having hard time using this to compile almost anything. I have set symbolic links with alternatives

p=x86_64-w64-mingw32
alternatives \
    --install /usr/bin/gcc.exe gcc /usr/bin/$p-gcc.exe 0 \
    --slave /usr/bin/ar.exe ar /usr/bin/$p-ar.exe

For example if I try to compile wget

./configure --without-ssl
make

Errors (edited for brevity)

connect.o:connect.c:(.text+0x3f): undefined reference to `__imp_htons'
connect.o:connect.c:(.text+0xbe7): undefined reference to `__imp_ntohs'
connect.o:connect.c:(.text+0xd96): undefined reference to `run_with_timeout'

If I use

MinGW shell with MinGW gcc
Cygwin shell with Cygwin gcc (gcc4-core)

Then Wget will compile.

Based off ak2 answer, this seems to work

./configure --host=x86_64-w64-mingw32 --disable-ipv6 --without-ssl
make

Solution

ak2 is partially incorrect as stated here.

The correct option is --host=x86_64-w64-mingw32, as you found out. --target is used for building a cross-compiler itself. The options are:

--build: What you are building on
--host: What you are building for
--target: If what you are building is a cross-compiler, what that cross-compiler will build for.