President Volodymyr Zelensky of Ukraine is planning to meet President Trump at the White House on Tuesday at a time when their relationship appears stronger than ever before — even as both men face challenges at home.

At the meeting, Mr. Zelensky, still confronting domestic fallout over sacking both his defense minister and army chief, will be hoping to reboot stalled peace talks in Ukraine’s war against Russia and to push for more U.S. help with weapons, particularly air defense. It’s likely, analysts say, that the men will also discuss the potential of a cease-fire in long-range airstrikes between Russia and Ukraine.

Mr. Zelensky will also attend the funeral of Senator Lindsey Graham, who died suddenly on July 11, hours after returning from Ukraine. The South Carolina Republican was perhaps Ukraine’s biggest ally in Mr. Trump’s circle, whose members have typically echoed Russian talking points.

Some analysts have speculated that Mr. Graham’s death might push Mr. Trump to be more sympathetic toward Ukraine. Some have also taken note of the visit this month to Ukraine by the right-wing activist Laura Loomer, part of the MAGA movement, who has recently expressed support for Ukraine.