President Zelensky is preparing to visit Washington on Wednesday, in what will be his first known trip outside Ukraine since Russia’s invasion began in February. Mr. Zelensky’s visit, while expected, could still be called off at the last minute due to security concerns.

The visit to Washington is set to include an address to Congress on Capitol Hill and a meeting with President Biden. It comes as lawmakers are set to vote on a year-end spending package that includes about $45 billion in emergency assistance to Ukraine and as America prepares to send Patriot surface-to-air missiles to the country to help stave off Russia’s invasion.

The latest tranche of American funding would be the biggest American infusion of assistance yet to Ukraine, above even Biden’s $37 billion emergency request, and would ensure that funding flows to the war effort for months to come.

Speaker Pelosi encouraged lawmakers to be on hand for Wednesday evening’s session. “We are ending a very special session of the 117th Congress with legislation that makes progress for the American people as well as support for our Democracy,” Ms. Pelosi wrote Tuesday in a letter to colleagues. “Please be present for a very special focus on Democracy Wednesday night.”

Zelensky has almost daily addressed various parliaments and international organizations by video and he has sent his wife to foreign capitals to drum up assistance. The visit comes a day after he made a dangerous trip to what he called the hottest spot on the 800-mile front line, the city of Bakhmut in Ukraine’s contested Donetsk province.

In a video released by his office from the Bakhmut visit, Mr. Zelensky was handed a Ukrainian flag and alluded to delivering it to American leaders. 

“The guys handed over our beautiful Ukrainian flag with their signatures for us to pass on,” Mr. Zelensky said in the video. “We are not in an easy situation. The enemy is increasing its army. Our people are braver and need more powerful weapons. We will pass it on from the boys to the Congress, to the president of the United States. We are grateful for their support, but it is not enough. It is a hint — it is not enough.”

Washington has committed nearly  $20 billion in security assistance to Ukraine since Russia launched its invasion on February 24, according to figures from the Pentagon. America is also providing intelligence to Ukrainian forces and helping Ukraine fend off Russian cyberattacks and efforts at sabotage, American and Ukrainian officials have said.

The visit comes at an important moment for Messrs. Biden and Zelensky as the White House braces for greater resistance from a Republican-controlled House that’s signaled it will put more scrutiny on aid for Ukraine in the new Congress. The House GOP leader, Kevin McCarthy, has said his party’s lawmakers will not write a “blank check” for Ukraine.

Inflationary pressures coupled with fears of a fresh wave of Ukrainian refugees in Europe have led some European leaders to cool on open-ended assistance for Ukraine. Mr. Zelensky recently told Britain’s prime minister, Rishi Sunak, that “he senses British support could decline,” a sentiment that might have been voiced in response to a BBC report that Mr. Sunak has asked for a data-driven audit on British military aid to Ukraine thus far.

Overall though, British support for Ukraine has remained steadfast and that is not likely to change. On Monday London announced a new $304 million aid package that according to a press statement from the prime minister’s office will include “hundreds of thousands of rounds of artillery” will ensure “a constant flow of critical artillery ammunition to Ukraine throughout 2023.”

Messrs. Biden and Zelensky frequently have held phone calls in coordination with the White House announcing new tranches of military assistance for Ukraine. The calls have been mostly warm, with Mr. Biden praising Ukraine for remaining steadfast against the Russians and Mr. Zelensky thanking the American president for support.

The one exception was a June phone call soon after Mr. Biden notified Mr. Zelensky another $1 billion package was headed to Ukraine. Mr. Zelensky didn’t miss a beat in listing additional assistance he said Ukraine needed. That irked Mr. Biden, who reminded Mr. Zelensky of the American people’s generosity.

The brief moment of tension hasn’t caused any lasting difficulty, according to officials familiar with the episode.

Mr. Zelensky addressed Congress by video link in March. Wearing a green T-shirt with the Ukrainian flag behind him, he argued that America and Ukraine shared common dreams and goals.

“Democracy, independence, freedom and care for everyone, for every person, for everyone who works diligently, who lives honestly, who respects the law,” he said then. “We in Ukraine want the same for our people. All that is a normal part of your own life.”

His visit comes in the final days of Ms. Pelosi’s House speakership. Republicans will take control of the House in January, while Democrats retain power in the Senate. 

While Republicans set to chair key national-security committees push for continued support of Ukraine, there are growing concerns among the GOP rank-and-file about the cost and duration of the effort.