The new package also calls for more action to protect children from pornographic and violent content online.
The Commission also proposes that video on demand services such as Netflix and Amazon should be forced to carry at least 20 per cent European content and significantly extends the scope of current legislation.
The strategy is the EU's latest step towards what is known as the digital single market, in which the EU's 500 million people will no longer be blocked from buying goods and services more cheaply from another member state online.
The measures must be approved by both EU governments and the European Parliament.
Reaction to the proposals continued on Thursday, with British Conservative MEPs welcoming the drive to make the digital single market fit for purpose.
But they expressed concern about the planned legislation which they believe would prevent online retailers "denying consumers in one country access to a site in another."
The group's internal market spokesperson Vicky Ford said: "In the traditional world we don't demand that retailers offer the same product at the same price in every market, so why should we try to do so online? Despite what the Commission is saying, many retailers are concerned this could be the consequence of the proposal.
"We must not put an unnecessary handbrake on the digital economy. We have to ensure any international legislation underpins, not undermines, it."
Further comment came from German MEP Evelyne Gebhardt, S&D group spokesperson for the internal market and consumer protection, who said, "We welcome these proposals and look forward to working with the Commission over the coming months."
She added, "Removing obstacles to the digital single market is a key priority for the group. We are pleased with the proposals to tackle unjustified geo-blocking - it is unacceptable that customers end up paying different prices or paying twice for the same service in different member states."
Greens/EFA group digital agenda spokesperson Julia Reda said, "The proposed 'anti-geoblocking' regulation doesn't do what it says on the tin. When most Europeans hear the term 'geoblocking', they think of the all-too-common error message that 'this video is not available in your country' - and yet the measures presented today will not do anything to address this.
"An anti-geo-blocking regulation that does not cover online video content misses the point," added the German deputy.
Elsewhere, industry representatives were equally quick to respond with Digital Europe, the Brussels based body which represents Europe's digital technology industry, saying it broadly welcomed the raft of proposals.
"It is reassuring to see that the Commission has reached similar conclusions to the tech sector and a majority of EU member states, in seeing online platforms above all as a force for good, rather than a threat," said John Higgins, director general of Digital Europe.
"However, we are concerned about the Commission's plans to monitor and potentially improve notice-and-action measures, as these could place an inappropriate responsibility on platforms to police the content on their services," he cautioned.
Business Europe's director general Markus Beyrer said, "Cross-border eCommerce in Europe is still underdeveloped with only 20 per cent of internet users buying online from other member states.
"Complex rules, remaining fragmentation and a lack of confidence are rightly addressed by the package presented. Still, we are concerned about the lack of clarity on certain elements of the geo-blocking proposal where loopholes may exist."
The European eCommerce and Omni Channel Trade Association, representing online trade across Europe, said it was "deeply concerned" about the "obligation to sell" element of the proposals.
Maurits Bruggink, its secretary general, said, "The Commission and policy makers risk creating new barriers in eCommerce by introducing an obligation to sell that triggers the applicability of various obligations on traders simply because of selling online, even if only domestically."