European leaders, gripped by a refugee crisis that has laid bare bitter divisions in their continent, agreed Wednesday to bolster their borders and increase aid to the refugee agencies stumbling under the burden of helping millions of people displaced by the war in Syria.

The commitment to devote at least $1.1 billion to fend off an escalating flow of refugees was a rare moment of unity for the squabbling 28 nations, but it was a sign that the one thing they could agree on was to keep people far from their borders. The emergency powwow came a day after an rare decision by Europe’s most powerful nations to override four holdout Central European countries and impose quotas for taking in asylum seekers.

With more than 477,000 people breaching the European Union’s borders this year, the crisis has proved to be a more profound challenge to the economic and political alliance than any in its history. More than Greece’s crisis earlier in the summer, which centered on the economic travails of a single nation, the flood of refugees has exposed disunity about Europe’s core values, with some nations saying that the continent is robust enough to welcome those in need and others saying that Europe itself is what needs protection.

So far, the solutions have been minuscule in comparison with the scale of the problem. The plan approved Tuesday to parcel out 120,000 asylum seekers across Europe represents just 20 days’ worth of new arrivals, and it gives few assurances that refugees will not simply take advantage of Europe’s open borders to flock to the wealthiest nations, such as Germany and Sweden.

Wednesday’s agreements were short on details, but they promised more help for the front-line nations along Syria’s borders that have taken in the most refugees. E.U. leaders also said they would build special receiving centers at their external frontiers to help sort those fleeing war from those coming for other reasons and increase funding for further border controls. And they promised a new push to achieve peace in Syria.

“If we don’t fight the root causes of flight, then people will say, and a very large number will say, that they want to resettle in places that offer more security to them,” said German Chancellor Angela Merkel after the meeting, which stretched nearly seven hours.

She said that among the efforts, she would support talks with Syrian President Bashar al-Assad in an attempt to bring peace to Syria, an apparent policy shift that was not shared by other leaders at the summit.

“One has to talk to many players. Assad is one of them,” Merkel said.

But E.U. leaders left many decisions to be made at their next summit Oct. 15. If asylum seekers keep arriving at current rates, that meeting will come after an additional 132,000 people reach Europe’s shores.

Frustrations over the meagerness of the continent’s response were clear from some of the leaders who gathered in the E.U. capital of Brussels on Wednesday to fight it out over dinner and drinks.

A look at the numbers behind the stream of refugees flowing into Europe as political leaders struggle to ease the burden. (Jason Aldag/The Washington Post)

“We should be talking about millions of potential refugees trying to reach Europe from Syria alone,” said European Council President Donald Tusk, in an implicit rebuke of the scale of the continent’s plans. “It is clear that the greatest tide of refugees and migrants is yet to come. Therefore we need to correct the policy of open doors and windows,” an apparent reference to Merkel’s open-door policy toward Syrians.

Her government’s August announcement that it would make it easier for Syrians to stay in Germany helped spark an even greater surge of asylum seekers toward Europe. But when Germany started to stumble from the influx, it reintroduced border controls, leaving a pileup of migrants in countries that did not want to take them in.

Other leaders were more pointed in their criticisms of the four nations – Hungary, Romania, the Czech Republic and Slovakia — that voted against the quota plan on Tuesday. European Union diplomats said that they had rarely heard such open criticism among E.U. leaders.

“Those who don't share our values, those who don't even want to respect those principles, need to start asking themselves questions about their place in the European Union,” said French President François Hollande as he entered the meeting. Afterward, he said there were still “tensions,” but that there had been less anger than in previous days.

The sharpest opposition to taking in more migrants has come from ex-Communist Central and Eastern European nations that have little recent history of newcomers or immigrants. Hungary has constructed a razor-wire-tipped fence along a 108-mile stretch of its southern border, and it is quickly expanding it. Slovakia said it would only take in Christian refugees before it said it would not take any at all, and Prime Minister Robert Fico said he would challenge the E.U. measures in court. The other three countries that voted against the plans Tuesday appeared resigned to accepting their quotas.

But anti-migrant sentiments have not been confined to the former Eastern bloc, surging widely across Europe. Far-right parties have campaigned against the newcomers in Scandinavia. One of Merkel’s conservative allies praised Hungary on Wednesday for helping to slow the influx.

As with the Greek euro crisis in July, many of the tensions were arising from idealistic policies to promote unity that stopped short of resolving the thorniest issues of national sovereignty. Europe created a common currency without unifying economic policies. It swept away borders without resolving differences in asylum and immigration policies. It has struggled to maintain a unified front against Russia amid the conflict in Ukraine.

The system worked in good times, but it has proven lacking during challenging ones.

“It has really struck to the core of, ‘What is Europe for if it can’t deal with these issues?’ ” said Raoul Ruparel, the co-director of Open Europe, a London-based think tank that pushes for E.U. reforms. “That’s a question that has long been asked in the U.K. but is now being asked in other parts of Europe.”

But with one set of discussions happening in Brussels on Wednesday, very different ones were happening further east in Europe, where a powerful river of refugees continues to flow toward Germany. For all Europe’s efforts to spread the migrant flow over more nations, many of the people on the road have a single destination in mind.

“Why would we go to Poland? Who knows anyone in Poland?” said Marwan, 29, a vegetable wholesaler from Daraa in southern Syria, who on Wednesday was in Vienna’s central station, waiting for a train to Salzburg, where he planned to disembark and walk over the Austrian border into Germany.

Refugees and migrants milled around the station, waiting for the next departures. Marwan, who asked to be identified only by his first name because he feared for the safety of family in Syria, said that he had uncles and cousins in Germany.

“I want to go to Germany. That’s it. That is where my family is,” he said.

Read more:

A global surge in refugees leaves Europe struggling to cope

The Arab world’s wealthiest nations are doing next to nothing for Syria’s refugees

As tragedies shock Europe, a bigger refugee crisis looms in the Middle East

Today's coverage from Post correspondents around the world

William Booth in Vienna contributed to this report.