BRUSSELS — European Union ministers were set to meet in an emergency session here on Tuesday to seek agreement on a plan that would force individual countries in the bloc to accept a share of the hundreds of thousands of refugees seeking asylum.

Migrants lined up to register at a camp after crossing from Greece to Macedonia on Tuesday.

The home affairs and justice ministers are gathering in Brussels for their second such session in eight days and are haggling over a proposal to distribute across the bloc an additional 120,000 refugees, only a fraction of those flowing into Europe. Germany alone has said it could receive a million asylum seekers this year.

To reach a deal, the officials must overcome months of squabbling that has highlighted the lack of a united European response to one of the worst humanitarian crises in decades.

France and Germany back a compulsory approach to resettling refugees from countries like Syria and Eritrea across the Continent. The idea is to relieve the pressure on front-line nations like Italy and Greece, where the migrants have been arriving in large numbers.

But some other countries, like the Czech Republic and Hungary, strongly oppose that plan on the grounds that it would encourage still more people to make hazardous journeys to Europe. Those countries also say they do not want to be transit zones for those who want to live in richer and more welcoming places like Germany and Scandinavia.

Another factor holding up a deal is the reluctance of a number of countries to hand over control of immigration to the European Commission, the Brussels-based executive agency for the European Union, which drew up the plans for the mandatory system.

Diplomats failed to agree on a draft accord on Monday but were expected to gather on Tuesday to try again before the ministers’ meeting, which was expected to begin at 2:30 p.m.

Representatives from countries that favor the plan could decide to pass the measure by a majority vote later Tuesday. But doing so would risk imposing an unworkable system on countries that have balked at accepting quotas of migrants. Putting in place the system without broad agreement would also exacerbate the disharmony in Europe that has already led to the reintroduction of border controls by some countries.

If the ministers fail to strike a deal, the discussion about the relocation of migrants is expected to spill into Wednesday, when European Union leaders are to gather in Brussels to discuss a wider response to the crisis.

Donald Tusk, the president of the European Council, which convened the meeting planned for Wednesday, said he wanted the leaders to discuss expanding cooperation with Turkey so that migrants in that country are given adequate care and shelter, and are dissuaded from trying to enter the European Union.

“We must help Syrian refugees to a better life closer to their homes”, — Mr. Tusk wrote on Twitter on Sunday.

Mr. Tusk also said he wanted the leaders to discuss expanding fingerprinting and creating more reception centers inside Greece and Italy. That could turn so-called hot spots where migrants would be gathered into fully fledged refugee camps.

One of the most intransigent countries in the migration crisis has been Hungary, which has become a front line for migrants seeking asylum elsewhere like Germany. The government in Budapest has already built a razor-wire fence along its border with Serbia, is bolstering its border along Croatia and has granted its army extra powers to deal with migrants, including allowing the use of tear gas, rubber bullets and other weapons, provided no lethal force is used. Hungary is also resisting the relocation plan — even though the proposal would allow it to move an estimated 54,000 migrants from its territory to other European Union members.

The Hungarian Ministry of Foreign Affairs said that the foreign minister, Peter Szijjarto, would travel to Turkey on Tuesday to present a Hungarian proposal calling for the European Union to finance refugee camps in Jordan, Lebanon and Turkey. The hope is that if the bloc works to improve the conditions in those countries, the refugees would be less likely to undertake the difficult journey to Europe. But it remains to be seen how a proposal by Hungary, a country that has railed against a perceived threat of a Muslim invasion, will be received in Turkey, a majority-Muslim country, which has hosted millions of the refugees.

In a further sign of the acrimony that has characterized the European debate on immigration, Prime Minister Viktor Orban of Hungary warned on Monday that his country was being overrun. “The migrants are not just banging on our door; they are breaking it down,” he said. “Our borders are in danger, our way of life built on respect for the law, Hungary and the whole of Europe is in danger.”

The debate at the ministers’ meeting on Tuesday is over a program for relocation of a further 120,000 asylum seekers — still only a small part of the total — that would be compulsory for most member countries.

An idea being discussed by diplomats to break the deadlock is to include in the final agreement the number of migrants member states would take, but to leave out the method used by the commission to make the calculations.

Even so, a deal on Tuesday could prove elusive.

“Some solutions are on the table, what is missing is the political will and leadership to see them through”, — John Dalhuisen, the Europe director for Amnesty International, warned on Monday.