Markku Niskala, head of the International Federation of Red Cross and Red Crescent Societies, said:"The drug resistance that we are seeing now is without doubt the most alarming tuberculosis situation on the continent since World War Two."
"Our message to EU leaders is: Wake up, do not delay, do not let this problem get further out of hand."
About 450,000 people get infected with tuberculosis each year in and around Europe, including Eastern Europe and Central Asia, said Pierpaolo de Colombani, a medical officer for the World Health Organisation (WHO).
Almost 70,000 of these cases have contracted strains that are resistant to the two main tuberculosis drugs, raising fears the disease could lead to epidemics in Western Europe on the scale of that seen in the 1940s.
The explosion in multi-drug-resistant tuberculosis, rooted in patients not taking the full course of their drugs, has meant that Europe is "nowhere near to being on track" to meet global targets on controlling the disease, said Michael Luhan of the Red Cross and Red Crescent federation.
The WHO has estimated that donors need to triple spending levels to $56 billion over 10 years to halt the global spread of the respiratory disease.
"Tuberculosis has always been low on the EU agenda"
Michael Luhan, Red Cross and Red Crescent Federation
Luhan said EU states had become too complacent about the disease in recent years, despite high rates of infection in neighbouring countries such as Russia, Ukraine, Romania, Belarus and Turkey.
"Tuberculosis has always been low on the EU agenda," Luhan told journalists in Geneva, where health experts are this week meeting to find ways to confront Europe's tuberculosis threat.
EU expansion alone will multiply the region's tuberculosis exposure, he said.
Migration from Eastern Europe and Central Asia will also raise risks of drug-resistant strains spreading in cities such as London, where tuberculosis infection rates have been steadily climbing over the last decade.
Some countries, including Latvia, have also been found to have cases of extreme drug-resistant tuberculosis - which does not respond to at least three of the six existing classes of second-line tuberculosis drugs - though De Colombani said the exact extent of this threat was not yet known.
The European Centre for Disease Prevention and Control and more than 20 other health agencies and non-governmental groups have urged European governments to intensify their tuberculosis fight.
"The hottest zones of drug-resistant tuberculosis are all around the periphery of the EU," said Mario Raviglione, director of the WHO's Stop TB division.
"Investment in tuberculosis control must reflect the real emergency we are facing and be placed higher on the European agenda, especially in donor countries," he said.