\documentclass{article}

\newcommand\mycommand[1]%
  {test:command arg=#1 environment arg=\myenvArg}

\newenvironment{myenvir}[1]
  {%
    \def\myenvArg{#1}%
    \begin{center}%
  }
  {%
    \end{center}%
  }

\begin{document}

\begin{myenvir}{Hello}
\mycommand{World}
\end{myenvir}

\end{document}