The two leaders met in the White House on November 7, where Trump granted Orban a one-year exemption from US sanctions on Russian energy, staving off a price surge that would have hit Hungary's economy hard, Orban has said.
In his letter, Trump said Orban's "bold leadership" served as an example for the rest of the world. Trump also said he looked forward to "deepening cooperation" on defence, energy and illegal migration.
"You have always stood firm to defend the principles that make Hungary such a tremendous place - faith, family, and sovereignty," Trump wrote in the letter dated December 10.
Nationalist Orban is facing what could be the toughest challenge to his 16-year rule from a combination of Hungary's economic stagnation, a jump in the cost of living and a juvenile centre abuse scandal that have boosted an opposition rival whose party leads most polls.
The election will probably be held in April.
In November, the two leaders also discussed forms of financial assistance, although Trump last month dismissed Orban's claim that Washington had already agreed to extend financial assistance to Hungary worth as much as $20 billion.
Orban said on Monday at a press briefing that Hungary had not managed to secure the type of financial support it had originally sought from Washington, but talks on a possible backstop were continuing.
In his letter, Trump also thanked Orban for an invitation to visit Hungary and said that his team would "be in touch" about his schedule.On Monday, Orban said that a visit from a "high-ranking" US politician was likely ahead of the election.
(Reporting by Krisztina Than and Anita Komuves; Editing by Philippa Fletcher and Kate Mayberry)
A handout photo made available by the Hungarian PM?s General Department of Communication shows Hungarian Prime Minister Viktor Orban holding a year-commencing international press conference in his office in Budapest, Hungary, 05 January 2026. PM Orban is flanked by Gergely Gulyas, Minister heading the Prime Minister's Office (L), and Zoltan Kovacs, State Secretary in charge of International Communications and Relations at the Prime Minister's Cabinet Office. EPA/Akos Kaiser HANDOUT HANDOUT - EDITORIAL USE ONLY - NO SALESHUNGARY OUTHANDOUT EDITORIAL USE ONLY/NO SALES