Version No. 1
You could do it as you would when using an environment with \fonttfp ... \endfonttfp
, what would give you this:

\documentclass{scrartcl}
\usepackage[utf8]{inputenc}
\usepackage[english]{babel}
\newenvironment{fonttfp}{\fontfamily{cmtt}\selectfont}{\par}
\begin{document}
\begin{itemize}
\item[] {\fonttfp Afghanistan Albania Algeria Andorra Angola Antigua and Barbuda Argentina Armenia Australia Austria Azerbaijan \endfonttfp}
\end{itemize}
\end{document}
Version No. 2
You could do it the LaTeX way (\begin{fonttfp}...\end{fonttfp}
):
\documentclass{scrartcl}
\usepackage[utf8]{inputenc}
\usepackage[english]{babel}
\newenvironment{fonttfp}{\fontfamily{cmtt}\selectfont}{\par}
\begin{document}
\begin{itemize}
\item[] \begin{fonttfp}Afghanistan Albania Algeria Andorra Angola Antigua and Barbuda Argentina Armenia Australia Austria Azerbaijan\end{fonttfp}
\end{itemize}
\end{document}
Version No. 3
Use a command.
\documentclass{scrartcl}
\usepackage[utf8]{inputenc}
\usepackage[english]{babel}
\newcommand{\fonttfp}[1]{\begingroup\fontfamily{cmtt}\selectfont#1\endgroup\par}
\begin{document}
\begin{itemize}
\item[] \fonttfp{Afghanistan Albania Algeria Andorra Angola Antigua and Barbuda Argentina Armenia Australia Austria Azerbaijan}
\end{itemize}
\end{document}
Version No. 4
Do the same as in (3), but without argument and add \par
manually.
\ttfamily
? Your current use of\fonttfp
will always result in an error, because the environment isn't ended (formally there's no\endfonttfp
), but as you use it it should be a command.