Unable to exchange JWT token into AWS credentials

Hi, I want to configure a machine-to-machine connection. I created cognito user pool as a identity provider and also Cognito identity pool. Then I configured it together, and set client_credentials as "OAuth 2.0 grant type" following the AWS docs. Then in postman I am able to get access token using /token endpoint but this token cannot be used to get cognito identity id (GetId API call) because of the following error:

An error occurred (NotAuthorizedException) when calling the GetId operation: Invalid login token. Missing a required claim: aud

I also tried AssumeRoleWithWebIdentity but it also fails. I guess I need id_token not access token but don't know how I can obtain that.