Relations with Zelenskiy have warmed as Ukraine has blunted Russian advances, while Netanyahu arrives amid growing White House frustration over the lack of progress towards a broader settlement in the Iran conflict and criticism from some of Trump's supporters who oppose deeper US involvement in the Middle East.
The two men are in Washington to attend a memorial service for senator Lindsey Graham, a hawkish Republican who was one of Trump's closest allies and who frequently tried to coax Trump into providing more support for Ukraine's war.
Both the Ukraine war and widening Middle East conflict are at critical junctures.
After the collapse of a ceasefire in the Iran war, Trump says he has paused US air strikes to give diplomacy another chance.
Zelenskiy, meanwhile, has been buoyed by Ukraine's recent successes.
Still, there is no end in sight for either conflict.
Netanyahu has run hot and cold with Trump, who at times has had to rein in the Israeli leader from attacking targets in Lebanon to try to weaken Iran-backed Hezbollah militants.
An acrimonious phone call in June in which the president called the prime minister "f***ing crazy", laid bare the strains between the two leaders.
Sources familiar with the matter said Netanyahu - who is struggling in the opinion polls - aimed to get Trump's support for his re-election campaign before an October 27 vote.
A White House official said Trump would discuss the conflict in Iran as well as tensions between Israel and Lebanon, whose president Trump hosted on July 21.
The official said they would also discuss the Abraham Accords, the agreements Trump brokered to normalise diplomatic relations between Israel and the United Arab Emirates, Bahrain, Morocco and Sudan.
Trump wants to add Saudi Arabia to the accords and conditioned a civilian nuclear co-operation deal with the kingdom on Riyadh signing up.
Riyadh has rejected joining the accords without a path towards Palestinian statehood.
Zelenskiy and Trump clashed repeatedly in the early months of Trump's second term, but relations between the two have improved in recent months as Ukraine has had greater success in the war, including with increased attacks on Russia's oil industry.
Zelenskiy was expected to have a short private meeting with Trump at the White House, said a source familiar with the plans.
Zelenskiy is expected to press Trump for urgently needed air defence capabilities, with Patriot missile interceptors a top priority, including Trump's promise to grant Ukraine a licence to produce them itself.
Zelenskiy has spoke with US envoys Steve Witkoff and Jared Kushner about the prospects for renewed peace talks with Russia and said Ukrainian and US officials could meet in the coming days.
