With fighting still raging in Ukraine, and a front line that has barely shifted in more than a year, the country’s president, Volodymyr Zelensky, headed on Tuesday to the World Economic Forum in Davos, Switzerland, amid a swirl of diplomatic discussions about possible peace talks.

Mr. Zelensky, dressed in olive green pants and a black crew-neck sweater, was greeted with applause when he walked onstage in a room packed with hundreds of people at the forum, a high-profile gathering of business and financial elites.

In his speech, he promoted a Ukrainian peace plan and called for stiffer sanctions on Russia. But in a contrast with his comments to the forum last year, Mr. Zelensky made no direct appeals for weaponry for new offensives on the battlefield.

“We need you in Ukraine to build, to reconstruct, to restore our lives,” he told the audience of investors. “Each of you can be even more successful with Ukraine.”

Mr. Zelensky highlighted his country’s plan to end the war, an initiative called the Peace Formula, which has gained the backing of dozens of countries. But those countries do not include Russia, and Moscow has rejected its terms.

Russia has signaled through informal envoys that President Vladimir V. Putin is now open to cease-fire talks. But Ukrainian officials have said that they will reject any temporary truce that comes separate from a broader settlement, lest Russia merely use the pause to regroup and attack again.

Russia, Mr. Zelensky said, has become an agent of chaos in world affairs, sowing instability in African nations, in Syria and in Ukraine through military interventions that attempts at negotiations have failed to slow. A cease-fire in the long-running war in eastern Ukraine did not stop the full-scale invasion in 2022, he said.

“I don’t believe Putin is capable of changing, only humans can do that,” Mr. Zelensky said.

On Monday, Switzerland agreed to push the Ukrainian plan a step forward. Switzerland will host a summit of countries backing the Peace Formula later this year, the country’s president, Viola Amherd, said after a meeting with Mr. Zelensky.

The plan calls for a full Russian withdrawal from all Ukrainian territory, including Crimea; payment of reparations; and prosecution of war crimes. All of those demands are considered, by analysts and even politicians backing the proposal, to be unreachable given the current balance of forces on the battlefield. The proposal also includes intermediary steps, such as securing Ukrainian nuclear sites, ensuring grain exports and exchanging prisoners of war.

The war in Ukraine has been a notable, but not dominant, topic in Davos this week. Government officials and business executives from across Europe and around the world have continued to express support for Ukraine and voice concerns that it is losing outside financial support at a critical time, but they have also pushed publicly and privately for a diplomatic end to the war.

Ukraine representatives and allies have worked hard to keep the war top of mind for attendees, staging a series of events in a temporarily converted storefront along the main promenade in Davos.

Sasha Ustinova, a member of the Ukrainian Parliament, spoke at a bipartisan gathering of American members of Congress on Monday night. “Ukraine will not make it without the support of the world and especially the United States,” she said.

She added: “I just want to be honest with you: I think everyone thinks Ukraine is winning. We’re going to lose without you.”

In a speech Tuesday afternoon in Davos, Jake Sullivan, President Biden’s national security adviser, said he and Anthony Blinken, the secretary of state, met with Mr. Zelensky earlier in the day.

Mr. Sullivan said he told Mr. Zelensky that “The people of Ukraine are steeled for the struggle ahead. And the United States and our partners will continue to stand with them.”

Ukraine is now on the defense along nearly all of the 600-mile front line and is facing wavering support from allies in Europe and in the United States for continued military and financial aid. It is preparing for an unpopular draft of about half a million more men into the army.

And the success of Donald J. Trump, who has opposed aid to Ukraine, in the Republican primary in Iowa on Monday signaled the start of an American presidential campaign in which Ukraine’s leverage in possible talks will rise and fall with Mr. Trump’s prospects of winning a second term.

If Mr. Trump’s prospects appear to improve, pressure could rise in Ukraine to push for swift, if risky, military progress while U.S. backing lasts or to seek settlement talks, said Cliff Kupchan, chairman of the Eurasia Group, a political risk assessment firm in Washington. “The smell of the coffee may become stronger in Kyiv,” he said.

The Swiss foreign minister, Ignazio Cassis, has suggested that Russia should be invited to the Peace Formula meeting even if Moscow was unlikely to accept.

The Ukrainian plan represented only one side in the war, Mr. Cassis said at a news conference on Sunday, and Russia’s positions would have to be heard eventually. It would be an “illusion,” he added, to think that Russia would participate on the terms Ukraine has laid out.

Mr. Zelensky said last month that Ukraine would engage with Russia by conveying, via an intermediary, the settlement proposal after a meeting of leaders backing the plan.

That formulation is a slight revision to his previous insistence that Ukraine would only negotiate after liberating its territory. Russia now occupies about 20 percent of Ukraine.

Mr. Zelensky said that 83 countries had participated in a conference of national security advisers on Sunday in Davos to agree on a final draft of the peace proposal. “For us, it is very important to show the whole world is against Russian aggression and the whole world is for a just peace,” he said.

Ukraine introduced the plan in 2022 and has been seeking to build support ever since. After the meeting of national security advisers, Ukrainian officials rejected, as they have done repeatedly, the possibility of talks that would lead to a cease-fire freezing the current frontline in place.

Mr. Zelensky visited Switzerland a day after his military claimed a success in the air war by shooting down a Russian airborne radar plane and damaging a command-and-control aircraft.

Ukraine hit both planes as they flew far behind the frontline over the Sea of Azov, an air force spokesman, Yurii Ihnat, told Ukrainian news media, suggesting a capability by the country to strike at long ranges. The military did not clarify what weapons it had fired. The Ukrainian claim could not be independently confirmed.

The radar plane, a model known as an A-50, crashed, while the command-and-control airplane, an Il-22, landed at an airport in southern Russia while on fire, Mr. Ihnat said.

Last month, the Ukrainian Air Force said that it had shot down five Russian fighter jets near the frontline, also without specifying how it had done so. Military analysts suggested that Ukraine had downed the aircraft with American-provided Patriot missiles.

Marc Lacey and Jordyn Holman contributed reporting from Davos.