BRUSSELS — European Union leaders ended an emergency summit meeting on Wednesday saying that they had calmed divisions over a migrant crisis and agreed to increase financial support for displaced Syrians in the Middle East.

“All of the conditions for a comprehensive solution of the refugee problem are not yet in place but we have gone a necessary step forward,” Chancellor Angela Merkel of Germany said at a news conference after the meeting.

The leaders of the 28-nation European Union were gathered in Brussels a day after ministers endorsed a bitterly contested plan to spread 120,000 asylum seekers around Europe, even to countries that do not want them.

Four Eastern European countries, including Hungary and the Czech Republic, voted against that decision in a sign that the usual consensus in European Union affairs has broken down as member states quarrel over how to manage the migrant crisis.

At the conclusion of the meeting early Thursday morning, the leaders said they would raise 1 billion euros, or about $1.1 billion, for Syrian refugees in the region and channel that money through the United Nations refugee agency and the World Food Program.

Continue reading the main story Graphic The Scale of the Migrant Crisis, From 160 to Millions The latest E.U. proposal addresses just a fraction of a human crisis numbering in the millions.

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“The more money we give, we inject, for example in fighting the root causes of flight, the less people will be forced to leave their home,” Ms. Merkel said.

There also needed to be “an intensive dialogue with Turkey,” she said. “Protection of the external border of the union is not possible without winning over the Turks as our partners.”

The leaders also debated giving more money and power to Europe’s border control agency, Frontex, and talked about how to dissuade people from attempting often dangerous journeys to Europe in the first place.

Earlier in the day, a top representative of the bloc said that the crisis could still grow much worse.

The official, Donald Tusk, the president of the European Council, the body that organizes European Union summit meetings, issued the stark warning in what appeared to be an effort to spur leaders to common action.

“Conflicts in the Middle East, especially in Syria and Iraq, will not end anytime soon,” Mr. Tusk told reporters ahead of the meeting. Eight million people are displaced inside Syria, and four million people have fled Syria to other countries, notably Jordan, Turkey and Iraq, he added.

“This means that today we are talking about millions of potential refugees trying to reach Europe, not thousands,” he said.

Mr. Tusk had called the summit meeting as part of an effort to restore some harmony and to forge a united response from fractious leaders as they confront a refugee crisis that has deeply divided the European Union and added fuel to already surging populist politicians who are hostile to immigration.

That strategy appeared to have been at least partly successful.

Mr. Tusk told a separate news conference after the meeting that there were still disagreements but that the “blame game” had been stopped.

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Ms. Merkel indicated that the anger apparent a day earlier over the plan to redistribute migrants had been kept under control during the meeting that began on Wednesday. Further discussion of that plan “did not play a role today,” she said.

Even so, tensions surfaced on Wednesday when Viktor Orban, the prime minister of Hungary, criticized Greece for failing to do enough to police its borders and prevent unregistered migrants from traveling northward.

If the Greeks could not manage their frontiers, then the European Union should help them do so, he said.

“I think if the Greeks are not able to defend their own borders we should ask kindly, because Greece is a sovereign country: Let the other countries of the European Union defend the Greek border,” Mr. Orban told reporters ahead of the summit meeting.

Hungary is among the countries to have taken the toughest stance in the crisis, including building a razor-wire fence along its border with Serbia to stop uncontrolled entry by migrants onto its territory.

Asked about Mr. Orban’s approach to the crisis, President François Hollande of France suggested ahead of the meeting that Mr. Orban was out of step with European Union values.

“Those who do not share these values, those who do not want to respect these principles, must question their presence within the European Union,” Mr. Hollande told reporters.

Ms. Merkel also offered thinly veiled criticism of Mr. Orban’s policies of sealing Hungary’s borders. “Setting up fences among member countries I think is not a solution to the problem,” she told the news conference after the meeting.

The decision on Tuesday to spread migrants across the European Union aims to resettle 15,600 asylum seekers from Italy and 50,400 from Greece — a total of 66,000 people — during the next two years.

European leaders left open an option to use the remaining reserve of 54,000 people to relocate migrants from other member states besides Greece and Italy in case there are sudden inflows in other parts of the European Union within the next year.

Hungary refused an earlier offer for migrants on its territory to be relocated, but must now take 1,294 people. Under the original European Commission plan, Hungary would have taken none.

Slovakia, which also balked at the plan, must take 802 people.

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