For Ukrainians living through war, the cost of the conflict is hard to measure: Thousands of people killed, countless homes and buildings destroyed by missiles, families displaced, livelihoods lost. But international leaders are gathering in the lakeside Swiss town of Lugano for a second day on Tuesday in an attempt to do just that.

The leaders, joined by aid organizations and financial institutions, are mapping out the monumental effort it will take to rebuild war-battered Ukraine.

Nearly five months of war has damaged crucial infrastructure — factories, airports, railway stations — and obliterated residential buildings, schools, hospitals, churches and shopping malls. And the bombs continue to fall. Ukraine’s prime minister, Denys Shmyhal, told those assembled in Lugano on Monday that the cost of rebuilding was estimated at $750 billion.

President Volodymyr Zelensky of Ukraine had warned the conference that the task of rebuilding the country would be “colossal.” Russia’s indiscriminate shelling was an attempt not just to destroy Ukraine but also the vision of democracy and Europe, he said by video link, making the war “not just ours, not just a local one.”

“This is Russia’s attack on everything that is of value to you and me,” he added. “Therefore, the reconstruction of Ukraine is not a local project, not a project of one nation, but a joint task of the entire democratic world.”

He reiterated that message in his nightly address to Ukraine.

Whatever the cost, Ukraine’s international allies will face an uphill struggle to help reconstruct a former Soviet state with a culture of endemic corruption and fragile democratic institutions. Transparency International, an anticorruption watchdog, ranked Ukraine 117th out of 180 countries on its corruption index in 2020.

At the same time, while more pledges of aid would be welcomed by Ukraine, many Western countries and their publics are suffering from war fatigue amid spiraling inflation and food and gas prices. And it remains to be seen how far countries will be willing to go to help Ukraine when the war finally ends.

Earlier this year, donor pledges for Afghanistan and Yemen fell far short of targets set by the United Nations. In Afghanistan, where the Taliban’s policies have complicated aid efforts, the U.N. said that $4.4 billion was needed this year in humanitarian aid alone, but $2.4 billion was raised. Of the $4.3 billion sought for Yemen, $1.3 billion was contributed.

Mr. Zelensky sent Mr. Shmyhal and other members of his cabinet to Lugano, a picturesque lakeside town, for two days of talks with a cast of international heavy hitters. Also in attendance were the president of the European Union’s executive arm, Ursula van der Leyen, who called the rebuilding of Ukraine “a generational task,” and the British foreign secretary, Liz Truss, along with senior officials from Europe, North America and Asia and representatives of major international financial institutions.

The meeting was planned long before the war as one in a series of conferences focused on tackling corruption in Ukraine. But after Russia began its invasion on Feb. 24, the focus shifted to recovery. The first lady of Ukraine, Olena Zelenska, also addressed the Lugano conference by video link on Monday and announced another meeting of first ladies and gentleman from around the world on July 23. She held the first summit of the group last year in Kyiv, the capital.

“Any discussions about the postwar recovery of Ukraine do not make sense if they do not prioritize the recovery of people’s moral and physical health,” said Ms. Zelenska in her address on Monday.

The Lugano meeting is still looking at issues of governance and corruption, which have taken on a renewed prominence in recent weeks: When the European Union accepted Ukraine last month as a candidate for full membership, it said that progress on corruption and the rule of law would be required to advance the application.

But even before the conference got underway, a number of countries seemed ready to promise financial support.

Britain said it would provide more than $1 billion for World Bank loans and fiscal support grants and guarantee World Bank loans for a further half-billion dollars, along with immediate support for land-mine clearance and rebuilding Ukraine’s energy infrastructure.

Vivek Shankar contributed reporting.

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