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\fonttfpwill 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. – TeXnician May 05 '17 at 15:52