I tried all solutions above (Native, changing url of VCS repository, updating Git, updating IDEA, invalidating Caches), but nothing helped me. Finally I found solution that works for me.
SOLUTION: I closed Idea and replaced content of file ~\.IntelliJIdea20xx.x\config\options\git.xml
with this:
<application>
<component name="Git.Application.Settings">
<option name="SSH_EXECUTABLE" value="IDEA_SSH" />
</component>
</application>
Then I started IDEA, try to checkout SSH GIT repository and it works and existing projects works as well. Interesting fact is that when I switch to NATIVE in Idea Settings, repository not working.