The countries of Europe, which together represent the world’s third-largest industrial emitter, are set to decide on Thursday whether they can leap to a future largely free of fossil fuels within the next 30 years.

Leaders from all 28 countries of the European Union are in Brussels this week, and analysts following the meeting said a large majority of countries were in favor of a proposal to get to net-zero emissions by 2050. The rules of the bloc, however, require that they reach a unanimous decision.

Several European Union countries have already announced such targets. Britain became the first among the 20 largest industrial economies to announce its net-zero emissions target this week; Sweden has a similar target. Finland and Norway have set the bar highest, resolving to reach the target by 2035.

Net-zero emissions, or climate neutrality, means slightly different things to each country. Norway and Sweden, for instance, aim to neutralize the emissions they generate (Norway is one of the world’s biggest oil producers, after all) by offsetting them by buying credits. Offsets could include things like funding clean-power projects in poor countries. That accounting method can neutralize a country’s carbon footprint but still allow the country to burn fossil fuels.

The European Union accounts for nearly 10 percent of global emissions. It includes countries that are fast transitioning to renewable energy, like Denmark, and those that retain a powerful coal lobby, like Poland.

Thursday’s meeting, the first since European elections this year, comes against a background of weekly student protests across Europe that are pressing leaders for urgent measures to stave off catastrophic climate change.

Europe has been walloped by extreme weather events that bear the fingerprints of climate change. Last summer’s heat wave across the Continent, for instance, was made five times more likely by climate change, one study concluded.

What the European Union countries are unlikely to agree on this week is to bolster their commitments made under the Paris climate agreement. Under that pact, the bloc pledged to slash greenhouse gas emissions by 40 percent from 1990 levels by 2030. The United Nations secretary general, António Guterres, has pressed countries to raise that target to 55 percent, according to a report published by Reuters.

Mr. Guterres is hosting world leaders at a climate summit at United Nations headquarters in September and leaning on many of them to announce more ambitious targets at his meeting.

A draft text of the European Union climate agreement, seen by The Times, does not include a provision to strengthen emissions-reductions targets.

The departing European Commission chief, Jean-Claude Juncker, last week cautioned against revising the bloc’s climate goals. “To fix new goals again and again doesn’t make sense,” he said. “Let’s focus on delivering what we’ve already got.”