The South Stream pipeline, financed by Russia's state gas giant Gazprom, would ship gas to western Europe via the Balkans, thus avoiding Ukraine.
But the European Commission says the pipeline may break EU competition rules and asked Bulgaria to suspend work.
Serbia's prime minister has denied his country has also halted building work.
Reports on Sunday had quoted Serbian ministers as saying the work was on hold until the EU, Russia and Bulgaria resolved their dispute.
But speaking on Monday, Prime Minister Aleksandar Vucic said no such decision had been made.
Serbia is in talks with the EU on joining the bloc. Bulgaria is already an EU member state.
Construction work on the South Stream pipeline began in Bulgaria in October 2013.
It is intended to deliver Russian gas to southern Europe without passing through Ukraine and if built, it would deliver 63 billion cubic metres of natural gas a year.
The project was initiated amid disagreements between Gazprom and Ukraine and Belarus over the pricing of Russian gas, which led to gas supplies to some parts of Europe being cut off. It took on added significance following the upheaval in Ukraine.
But the European Commission says Bulgaria may have broken EU public procurement laws by choosing local and Russian bidders for its part of the pipeline, and earlier this month, asked Bulgaria to stop work.
On Monday, Russia's EU envoy Vladimir Chizhov said the move by Brussels was a "creeping shift to economic sanctions against Russia".
"It is hard to shake off the feeling that the European Commission's blocking of the start of work on the construction of Bulgaria's key section of South Stream has been done for purely political purposes," Russia's Itar-Tass news agency quoted him as saying.
Bulgaria has previously said it is being targeted by Brussels as a means of retaliating against Russia over the situation in Ukraine.
Bulgarian Energy Minister Dragomir Stoynev said on Sunday that the project remained "irreversible and important for both Europe and Bulgaria" and that he was sure a solution would be found.
The EU and the US have imposed sanctions on a number of Russian individuals and companies following Moscow's intervention in Ukraine and its annexing of the Crimean peninsula, but Gazprom has not been targeted.
The firm supplies 30% of Europe's gas - some 15% via Ukraine - and has warned exports will be affected if sanctions are expanded.
Meanwhile, Gazprom has also threatened to cut supplies to Ukraine over an unpaid gas bill that it puts at more than $2bn (Â£1.2bn). This too would affect European supplies.

It happened at Pinewood Avenue in Woodburn. The man is understood to be a high-profile loyalist.
The ambulance service received a call about 14:15 GMT following reports of a man with a gunshot wound.
After treatment at the scene by paramedics, he was taken to the Royal Victoria Hospital in Belfast.
In the aftermath of the attack, armed police wearing protective masks carried out raids on property in the area.
There has been an ongoing feud between loyalist factions in Carrickfergus for some time.
It is understood one line of enquiry is that the shooting could be connected.
PSNI Supt Darrin Jones said that while the investigation was "still at an early stage police are following significant lines of enquiry".
"Firearms being discharged in a residential area, particularly during daylight hours when children are in the vicinity, is concerning," he added.
"We need the community to give us the information needed so we can remove the dangerous individuals who carried out this attack from our streets and put them before a court of law.
"There will be a continued police presence in the area as we search for those who carried out this brutal attack."
Alliance MLA for East Antrim Stewart Dickson said a "shooting is a very violent incident and it will undoubtedly have caused a great deal of fear and concern".
Ulster Unionist MLA John Stewart said he was "shocked" to hear of the attack and that there was "no justification for such actions".
Detectives are appealing for anyone with information to contact them on 101 or Crimestoppers anonymously by telephoning 0800 555 111.
Russia has accused the European Union of imposing "creeping" economic sanctions following Bulgaria's decision to halt construction of a gas pipeline.
[NEXT_CONCEPT]
A man in his 40s has been taken to hospital with life-threatening injuries after being shot in the neck in Carrickfergus, County Antrim.