Asking user to login to another website from within my app

I am working on an app which requires me to interact with an external API from an external website on behalf of the user. For this I need to ask them for their credentials for this other API. Will users refuse to login to the other website through my app due to security concerns? (Maybe that I would use their credentials for other malicious things).

I was thinking about performing the login through a Web View, this might make things look more natural for the user? Although I would prefer not using a Web View due to the platform I'm using to make the app does not support them very well.

Thanks