The Telegraph came second with 7.4 million web-only readers, while the Daily Mail dropped to third as the NRS reported 6.8 million web-only readers.
The Independent (4.16 million) and Mirror.co.uk (4.15 million) see out the top five in terms of readers who visit the website but do not read the print edition.
A Guardian News and Media spokesperson said: "Our digital first strategy and open approach places us at the forefront of media organisations who are adapting to changing habits in news consumption."
Every audited title except the Daily Star experienced a drop on reported figures on web-only readers, as online readership increased to just under one million each month.
In terms of year-on-year growth, the Daily Star was also the strongest performer with a 115 per cent increase on 0.32 million registered in June 2013, followed by the Daily Express, with a 92 percent increase, and the Metro (69 per cent).
The Sun and The Times, which both operate behind a paywall, saw the largest decreases in traffic year-on-year, dropping by 47.5 per cent to 0.21 million web-only readers and 67.7 per cent to 0.92 million readers respectively.
The only titles to have a larger online readership than print are The Independent, with 9.1 per cent more online readers; The Telegraph, with 81 per cent more readers online; and The Guardian, which more than doubles its net readership.
The Daily Mail still outperforms the competition where total readership is concerned, reaching 17.7 million readers through its print edition and website.
The NRS PADD report combines monthly figures from comScore with a monthly average of the annual data recorded by NRS. The reported figures are for adults aged over 16 in the UK.
Update: This article has been updated with a quote from Guardian News and Media
Additional reporting by Catalina Albeanu