"We in the United Kingdom value our links with Poland enormously," the prince told guests at the gala in Lazienki Park after standing for both national anthems and wishing everyone "good evening" in Polish.
The visit is not officially tied to British-EU diplomatic relations but British media outlets have dubbed it the "Brexit diplomacy tour".
London's shock decision to exit the European Union has been closely watched in Poland. There are nearly a million Poles in Britain, making them the biggest minority community from the EU, and their future remains unclear.
"There is much to celebrate about the warmth of our relationship today... Polish is now the second most spoken language in the United Kingdom, with a generation of young people growing up who feel both British and Polish," William added at the reception.
"Such links -- diplomatic, military, cultural -- offer much promise and opportunity for the future."
After landing in the Polish capital with their children Charlotte and George in tow, William and Kate walked through the old part of town shaking hands and posing for photos with fans carrying Polish and British flags.
Although the main goal of their visit appears to be a charm offensive by Britain, the programme also includes a heavy emphasis on history.
- Walesa, Holocaust and Airbus -
As guests of President Andrzej Duda and his wife Agata, the royal couple toured the Warsaw Uprising Museum earlier Monday.
On Tuesday, they will visit the Stutthof former concentration camp, which Nazi Germany set up in 1939 in what was then the free city of Danzig and is now the Polish city of Gdansk.
Also in the Baltic port city, Kate and William will visit the European Solidarity Centre museum, which tells the story of the Soviet bloc's only free trade union.
They will also meet freedom icon Lech Walesa, who won the Nobel Peace Prize as the leader of the Solidarity trade union and later became Poland's first democratically elected president after negotiating a bloodless end to communism for the country in 1989.
But William and Kate have also got a chance to experience modern-day Poland, as they met with young entrepreneurs at the top of a Warsaw skyscraper on Monday.
They will also tour the new Gdansk Shakespeare Theatre, where a meet-and-greet with actors dressed in Elizabethan costumes is planned.
Germany for its part will show Prince William, who is a helicopter pilot, the Airbus training centre and the assembly line of the Airbus A320.
The couple will also visit the Holocaust museum and attend a gala at the British ambassador's residence in Berlin.