Ukraine, having seized the initiative on the battlefield against Russia with its recent sortie deep into enemy territory, is looking to go on the diplomatic offensive as well.

The government of Ukrainian President Volodymyr Zelenskyy plans multiple briefings with the White House and the campaigns of the two presidential contenders in the coming days on a proposed agreement that would halt the fighting that began when Russian forces invaded in early 2022.

Russian officials have dismissed out of hand the idea of peace talks now, but the pressure may grow on President Vladimir Putin to at least respond as his forces struggle to evict Ukrainian troops from the widening swath of territory they hold in the Kursk border region.

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In recent months, Kyiv showed little interest in a cease-fire as its forces were on the back foot along the 600-mile front in eastern and southern Ukraine.

With the startling success of the Kursk operation launched on Aug. 6, Mr. Zelenskyy spoke this week more expansively than ever before of the outlines of a peace deal his government was willing to accept. He told reporters in Kyiv that the invasion of Russia was just the “first pillar” of a multistep process.

Ukrainian Defense Minister Rustem Umerov and presidential adviser Andriy Yermak were expected to arrive in Washington this week, The Associated Press reported. They were expected to press the Biden administration for greater freedom to use Western military aid in more offensive operations, such as the Kursk attack, although the new Ukrainian thinking on a peace deal could also be on the agenda.

The Ukrainian president said Tuesday that he planned to give President Biden and his aides a fuller briefing on the plan and that Kyiv was reaching out to the campaigns of Democratic presidential nominee Kamala Harris and former President Donald Trump, her Republican opponent, with control of the White House up for grabs in November.

The Ukrainian leader said Mr. Zelenskyy and Mr. Biden will be among the world leaders traveling to New York for the annual U.N. General Assembly the week of Sept. 22 and will likely meet then.

“The main point” of the diplomatic push “is forcing Russia to end the war,” Mr. Zelenskyy said in Kyiv this week. “We really want justice for Ukraine. And if this plan is accepted — and, second, if it is executed — we believe that the main goal will be reached.”

The Ukrainian offensive of recent weeks has already yielded one tangible return. Ukraine said it had captured nearly 600 Russian soldiers, and Kyiv and Moscow this week exchanged 115 prisoners of war on each side in a deal brokered by the United Arab Emirates. Mr. Zelenskyy has joked on social media that he was “grateful to each unit” — Russian POW — “that replenishes our exchange fund.”

Although Kyiv hoped its military success would persuade the Kremlin to negotiate, the Russian Foreign Ministry took the opposite tack. It refused any diplomacy while Ukrainian forces remained deep inside Kursk.

“This lawlessness is taking place with the full connivance of the West and its encouragement of the terrorist activities of the Kyiv regime,” Foreign Ministry spokeswoman Maria Zakharova told reporters in Moscow this week.

When Moscow’s forces were on the attack earlier this year, Mr. Putin proposed a peace agreement with terms certain to be rejected by Ukraine and its Western backers. The plan called for recognition of Russian-annexed lands in the occupied Donbas region, the withdrawal of all Ukrainian forces from the region, the end of U.S. and global sanctions on the Russian economy and a pledge that Ukraine would never join the NATO alliance.

On Wednesday, Russian Foreign Minister Sergey Lavrov accused Ukraine of placing unacceptable preconditions on any bilateral negotiations and said the U.S. and other countries were actively fueling Kyiv’s intransigence.

“The West is dissuading Ukraine from holding normal negotiations,” Mr. Lavrov told a news conference Tuesday while visiting Yemen. “It is doing everything it can to make Ukraine continue the escalation.”

In his remarks this week, Mr. Zelenskyy appeared to be discussing a more comprehensive package than Kyiv has previously been willing to consider. He said the Kursk operation was just the first step of the plan.

“The second [phase] is Ukraine’s strategic place in the security infrastructure of the world,” Mr. Zelenskyy said in an apparent reference to NATO and Kyiv’s place in the Western security sphere. “The third phase is the powerful package of forcing Russia to end the war in a diplomatic way, and the fourth phase is economical,” with the rebuilding of Ukraine’s battered economy and infrastructure projected to cost hundreds of billions of dollars.

The reconstruction cost went up this week after Russia launched a furious barrage of missile and drone strikes on successive nights, killing dozens across the country and targeting, in particular, Ukraine’s energy infrastructure. Fears are mounting that Ukraine’s power grid will be stressed as the cooler seasons approach.

AP reported that at least one Russian missile slammed into the heart of Mr. Zelenskyy’s home city on Wednesday, just as officials in Kryvyi Rih were observing an official day of mourning for an attack the previous day that killed four civilians at a hotel. The latest attack on the city struck civilian infrastructure, wounding eight people, officials said on social media.

• This article is based in part on wire service reports.