The president posted photographs on her Twitter account showing her with Trump and May holding red and white jerseys bearing their respective names in meetings at a NATO summit in Brussels.
Trump was given the number nine jersey of striker Andrej Kramaric -- that number was also worn by the top scorer at the 1998 World Cup, Davor Suker.
May received the number 10 jersey of Croatia captain Luka Modric.
After a dramatic win on penalties against hosts Russia, Croatia has repeated the success of the 1998 team which reached the semi-finals in the country's first World Cup as an independent nation.
They are hoping to go one better by beating England in Moscow to reach the final against France.
The country of about four million people has been gripped by football fever with squares packed with red-and-white painted fans, stalls selling football jerseys and flares, drivers blaring their horns and people hugging and singing -- scenes reminiscent of 1998.
Grabar-Kitarovic, a known football fan, attended Croatia's matches against Denmark and Russia.
About 10,000 Croatia fans are expected in the 80,000-crowd at the Luzhniki Stadium, including Prime Minister Andrej Plenkovic.