\documentclass{article}
\usepackage{fontspec}
\usepackage{polyglossia}
\setdefaultlanguage{russian}
\setmainfont[Ligatures=TeX]{Times New Roman}
\begin{document}
\section{Test}
\end{document}
I already tried what was suggested here. here, and here. Tried to compile with XeTeX and LuaLaTeX but the result is same.
And this font does support cyrillic script, the following compiles and looks properly:
\documentclass{article}
\usepackage{fontspec}
\setmainfont[Ligatures=TeX]{Times New Roman}
\begin{document}
АБВГД
\end{document}
\newfontfamily\cyrillicfont{Times New Roman}[Script=Cyrillic]after the\setmainfontcommand. See here for futher reference: https://tex.stackexchange.com/questions/91507/liberation-mono-the-current-roman-font-does-not-contain-the-cyrillic-script and https://tex.stackexchange.com/questions/223327/lualatex-xelatex-with-koma-for-cyrillics – Jasper Habicht Feb 05 '18 at 12:39