Speaking at a news conference after a parliamentary vote on the issue, she refuted claims that the draft law would undermine cultural differences between member states.
She said, "This has been said, not least by those who have lobbied, not always constructively, against this legislation. But, on the contrary, I think the opposite is the case."
Members of Parliament's internal market committee voted by 30 in favour of the draft geo-blocking law, with just two against.
It gives Thun, the rapporteur on the issue, a mandate to start three-way talks with the Council and Commission.
The draft rules seek to ensure that consumers buying goods from another EU country, whether online or in person, are not discriminated against on the basis of their nationality or place of residence or temporary location.
Once the new rules are enforced by member states, consumers will be able to video games or read eBooks, regardless of in which country they purchased their subscriptions.
Thun told reporters, "It means that we will see an end to those online messages that say things like 'access denied' or 'access blocked.' This can be very frustrating but this legislation will get rid of this unwanted hurdle."
The MEP said that while differences on the geo-blocking issue exist between member states, she is optimistic that a compromise will be reached in the trialogues that will start next month.
She is hopeful the draft will be formally adopted by Council before the summer recess and said an assessment will take place after three years with a view to it embracing other services, such as audiovisual.
She said, "I came under a lot of pressure from both consumer and business organisations and some of it was not very constructive. Some seemed happy to box countries in at their borders.
"It was argued that opening up the market in this way will undermine cultural diversity but this argument does not hold water. Operators will now, for example, have access to a much broader range of consumers."
She said, "This can only be advantageous for consumers. It will also boost Europe's competitiveness and help cut red tape."