If it is asking you for a username and password, your origin remote is pointing at the HTTPS URL rather than the SSH URL.
Change it to ssh.
For example, a GitHub project like Git will have an HTTPS URL:
https://github.com/<Username>/<Project>.git
And the SSH one:
[email protected]:<Username>/<Project>.git
You can do:
git remote set-url origin [email protected]:<Username>/<Project>.git
to change the URL.