The proposal the EU put forward was accepted by Serbia but rejected by Kosovo, High Representative Josep Borrell said.
The leaders of Serbia and Kosovo failed to reach a deal to end their row over license plates during an emergency meeting in Brussels on Monday.
After eight hours of talks, Serbia's Aleksandar Vučić and Kosovo's Albin Kurti "did not agree to a solution today," Josep Borrell said.
The bloc's top diplomat said the EU put forward a proposal that "Vučić accepted today but unhappily Prime Minister Kurti did not".
Still, he added, "both bear full responsibility for the failure of the talks today and for any escalation of violence that might occur on the ground in the following days."
Tensions between Pristina and Belgrade have flared up in recent months, threatening to become the most serious crisis between the two sides in recent years.
Kosovo, which remains unrecognised by Serbia and which is home to a majority ethnic Albanian population, wants some 10,000 Kosovo Serbs whose vehicles have Serbian-issued plates to replace them with Kosovo Republic plates.
The phased plan includes warnings, fines and eventually driving bans for refusing to switch plates with the total ban to come into force in April.
Serbs in northern Kosovo, who like Belgrade do not recognise Kosovo's 2008 declaration of independence from Serbia, refuse to do so.
Many have resigned from public institutions to protest the new provision, including hundreds of police officers. Borrell emphasised that this "leaves a very much dangerous security vacuum" on the ground.
The meeting in Brussels came as the deadline for the punitive measures to come into force is due to expire at midnight.
Serbia to 'act accordingly'
Borrell nonetheless called on the two sides to implement the proposal put forward by the EU and which calls on Kosovo "to immediately suspend further stages related to the re-registration of vehicles in north Kosovo and Serbia to suspend issuing new license plates which Kosovo cities denomination, including KM plates."
"This would allow space and time for the parties to look for a sustainable solution to the license plates issue," the High Representative argued.
Vučić said in a statement to journalists that the EU's proposal "was fine with us. We will respect and act accordingly."
"It is clear to everyone in the EU, but also in the world, who was constructive, who wanted an agreement and the preservation of peace. We only insisted that the signed agreements must be respected."
He will address the nation either on Monday evening or Tuesday.
Borrell added that he will inform member states and international partners about "the unconstructive behaviour of parties and complete lack of respect for their international legal obligations, and this goes in particular for Kosovo."
"This sends a very negative political signal," he went on.
"I made it very clear to both leaders that if EU accession is their ultimate objective, one to which they have both committed, we expect them to act accordingly with that. From my side, I will keep the dialogue very high on my agenda," he also said.