How to access private aws ecr registry from github actions?

We want to create a github actions workflow which will generate the docker image at the end and should push to aws ecr private registry.

If it is public registry, I can get the access directly from github actions. But with private registy as below, it is accessible through IAM policies only. I can give access to an ec2 instance.

But how to use this private registry in the github actions workflow?

I tried logging in with the user:AWS and password retrieved from aws cli.

But I am getting this error

Error response from daemon: login attempt to https://436380240297.dkr.ecr.us-east-1.amazonaws.com/v2/ failed with status: 400 Bad Request