osowskit is correct, the easiest way to do this is to iterate over the list of issues and the list of pull requests in a repository (I'm assuming you would like to get separate counts for each, reading between the lines of your question).
The issues API will return both issues and pull requests, so you will need to count both and subtract the number of pull requests from the number of issues to get the count of issues that aren't also pull requests. For example, using the wonderful github3.py Python library:
import github3
gh = github3.login(token='your_api_token')
issues_count = len(list(gh.repository('owner', 'repo').issues()))
pulls_count = len(list(gh.repository('owner', 'repo').pull_requests()))
print('{} issues, {} pull requests'.format(issues_count - pulls_count, pulls_count))
state=open- osowskitstate=openis the default for both listing issues and pull requests, so it's not necessary to specify it. - kfb