BRUSSELS — They discussed Greece’s bailout. They grappled with pension issues. They pored over draft budgets.

But Monday’s meeting of the Eurogroup, the 19 finance ministers from countries that share the euro, was most notable for what it did not address: the future of their president.

Jeroen Dijsselbloem, the Dutch finance minister and current president of the Eurogroup, has been one of the public faces of austerity in Europe. He has been praised for helping lay the foundations for the region’s economic recovery, but has been scorned for arguing in favor of fiscal restraint even as countries like Italy and Greece have struggled to overcome economic downturns.

Now, his fate is in doubt after last week’s election in the Netherlands. With his Dutch Labor Party recording a poor showing at the polls, he will probably lose his post as finance minister, meaning he will be replaced in the Eurogroup by the end of his term early next year.

The fight to fill the impending vacancy is likely to kick off a wave of jockeying among member states. The head of the Eurogroup plays an intensely political role, setting the tone for a bloc of ministers that presses individual governments to shore up their finances and grants political approval for bailouts.

Candidates are already being discussed, including Spain’s center-right economy minister and a Socialist member of the Slovak government. But whatever minister prevails, Germany, the region’s heavyweight economy, is still expected to dominate on issues like Greece’s bailout and regional budgetary rigor.

“Dijsselbloem has essentially been Germany’s agent in the Eurogroup,” said Mujtaba Rahman, the Europe director of the Eurasia Group, a political risk consultancy.

Mr. Dijsselbloem had been his country’s finance minister for a matter of months when he took over as head of the Eurogroup in early 2013, and his tenure had a rocky start.

An expert in agricultural economics who studied in Ireland and lives in the Dutch countryside, he incited controversy by endorsing a bailout of Cyprus that forced losses on many ordinary depositors.

Though Mr. Dijsselbloem conceded that he made mistakes, and the Cypriot government agreed to a revised deal that put a greater burden on richer depositors, the stage was set for even tenser negotiations with Greece.

By early 2015, Greece had been subject to years of tough austerity, and an increasing number of people were fed up with the seemingly never-ending belt-tightening measures sought by creditors. Thousands flocked to exuberant rallies against the country’s lenders.

In January of that year, Greeks voted in Syriza, a far-left party that campaigned on a broad pledge to roll back years of austerity measures, restoring cuts to salaries and pensions and securing a write-off of the country’s huge debt burden. At the center of that effort was Yanis Varoufakis, Greece’s combative finance minister.

At a joint news conference with Mr. Dijsselbloem in Athens, Mr. Varoufakis flatly rejected working with the so-called troika — the European Commission, the International Monetary Fund and the European Central Bank — which had jointly demanded spending cuts and tax increases in exchange for loans.

Those comments prompted a stony-faced Mr. Dijsselbloem to admonish his Greek counterpart for effectively seeking to derail the talks.

Behind closed doors, the atmosphere was even worse. In one meeting of finance ministers in February 2015, the pair called each other liars and nearly came to blows, Pierre Moscovici, the European commissioner in charge of economic and financial affairs, told a French journalist.

Then, after Mr. Varoufakis left a pivotal meeting in late June, the Eurogroup’s finance ministers continued to confer. Mr. Dijsselbloem said the session would proceed “without the Greek colleague,” declining to even use his counterpart’s name.

The clashes between the two men inspired a Dutch rap video, and although Mr. Varoufakis was replaced by Euclid Tsakalotos in July 2015, he remained critical in his references to Mr. Dijsselbloem, writing in April 2016 that they were never going to have “a beautiful friendship.”

Ultimately, the Eurogroup failed to reach a deal with Greece, and it fell to national leaders like Chancellor Angela Merkel of Germany and Prime Minister Mark Rutte of Holland to negotiate an agreement. Athens was forced to create a 50 billion euro, or $53.6 billion, privatization fund to help pay down debt in exchange for an international bailout, its third since 2010.

Mr. Dijsselbloem certainly presided over more than an unending series of crises.

The eurozone has expanded under his watch, with Latvia and Lithuania joining in 2014 and 2015. Eurogroup meetings have also run far more smoothly than under his predecessor, Jean-Claude Juncker, the current president of the European Commission, according to finance ministers and European officials.

And since the European Central Bank introduced an effective backstop in 2012, buying bonds from eurozone countries with distressed economies, the Eurogroup has also allowed countries like France and Italy significant fiscal leeway.

“Dijsselbloem is widely perceived as a good chair of the Eurogroup who has exercised a steady hand,” said Guntram B. Wolff, the director of Bruegel, a Brussels think tank.

But Greece has loomed large over Mr. Dijsselbloem’s tenure, and is likely to dominate his successor’s priorities.

The country’s debt still stands at 180 percent of gross domestic product, and nearly a quarter of the population is unemployed. The prospects for economic recovery remain bleak. Fearful of the political uncertainty caused by seemingly unending bailout talks, foreign investors have been wary of putting money into Greece.

More recently, Mr. Dijsselbloem has tried to forge a more equitable policy for the country, pushing for meaningful ways to ease its debt burden. Last year, he drafted a three-stage debt-relief plan that was eventually accepted, albeit only after it was watered down in the face of opposition from Germany.

The Dutch politician was “very austere” at the outset of talks with the newly elected Syriza government in 2015, said Georgios Kyrtsos, a conservative Greek member of the European Parliament. But he became “more constructive” as time went on, and Mr. Kyrtsos described him as “extremely capable.”

As a result, views of him improved. Anger toward Ms. Merkel or Wolfgang Schäuble, Germany’s finance minister, is much fiercer within Greece, and Mr. Dijsselbloem’s relations with Mr. Tsakalotos are a world apart from his confrontations with Mr. Varoufakis.

And while many in the country celebrated when his Dutch Labor Party suffered heavy losses at the polls, several Greeks were circumspect about who might replace him and whether such a swap would have any impact.

Germany holds outsize influence within the European Union, and in the Eurogroup in particular. Changing the bloc’s leader is unlikely to have much impact on decision-making in Berlin.

“He’s just a yes-man of Europe,” said Yiannis Garoutsos, 52, an electrician in Athens. “He was just doing Germany’s dirty work.

“They’ll find someone just as accommodating to replace him.”