Marchers greeted him with chants of "Czołem, panie prezydencie" ("Greetings, Mr President") and sang the national anthem.
Nawrocki is carrying a white-and-red flag, accompanied by his elder son and several senior presidential aides.
The march set off shortly before 3 p.m. local time from Dmowski Roundabout and is heading for the grounds of the National Stadium.
This year’s slogan is "Polak w Polsce gospodarzem" ("A Pole as host in Poland").
The annual demonstration has long been a source of controversy over nationalist rhetoric, and this year's slogan has further fueled debates surrounded by anti-immigration sentiment and political divisions.
Participants are wearing red-and-white scarves, hats and armbands, and carrying flags and banners bearing the names of towns from across the country.
Motorcyclists, historical re-enactors and vintage tractors are at the front, along with relics of St Andrew Bobola, a martyr.
Flares and smoke bombs continue to be set off along the route, despite a ban on pyrotechnics.
Drones are also barred over Warsaw on the holiday, as is carrying weapons of any kind, even unloaded.
Warsaw Mayor Rafał Trzaskowski had urged people to celebrate independence calmly and with dignity, saying safety was the priority.
Jarosław Misztal, director of the city’s Security Centre, said that as of mid-afternoon there had been no major incidents.
He said all city services were on full alert and that anyone using pyrotechnics could expect a heavy fine, with city CCTV used to identify offenders.
He gave no attendance figures, as people were still arriving.
Other events are under way in the capital, including a city-organised festival on Krakowskie Przedmieście and a separate registered assembly, due to end at the Sejm, the lower house of parliament.
Misztal said the routes do not cross and the distance between them poses no risk.
Trams and buses are not running along some central streets near Dmowski Roundabout.
(ał)
Source: PAP