Trump said he would have been willing to wait longer if necessary.
"There's no way we can be deterred," he said, shortly after taking the stage at 11:15pm on Saturday (1:5pm AEST Sunday).
Authorities allowed the crowd to return to an open field near the Washington Monument where Trump was due to speak, after ordering a weather-related evacuation that forced spectators to shelter in nearby museums and government buildings for a few hours.
Visitors had waited hours to get into the event, contending with stepped-up security and temperatures that reached 39C.
The record-breaking heat wave forced the cancellation of several parades and other events in the area.
"It's just part of the deal I signed up for," said Glen Solander, 60, a software engineer visiting from Sioux Falls, South Dakota, as he waited at a security checkpoint on Saturday afternoon.
Other visitors included the white nationalist organisation Patriot Front.
The group posted on social media that it had arrived in the capital, and hundreds of people wearing the group's outfits travelled to the city on Metro trains serving the District of Columbia region. Local police said they had not received any reports of violence.
Past presidents have generally avoided in-person appearances at July 4 celebrations, but Trump has blurred the line between official commemoration and campaign-style politics.
The Trump administration's Freedom 250 group has largely sidelined a nonpartisan body set up in 2016 to handle the 250th anniversary and has fenced off much of the 2.5km National Mall for a "Great American State Fair" featuring attractions such as a Ferris wheel alongside displays by conservative groups and defence contractors.
Freedom 250 says the fair aims to showcase the people and innovations that make the US "the greatest nation on Earth".
Several Democratic-led states declined to send delegations, and many performers scheduled to appear dropped out, citing concerns about partisanship. Trump opened the event with a rally on June 24.
Crowds were sparse at first but have swelled in recent days, forcing visitors to wait in entrance lines that stretched several blocks.
Other activities with Freedom 250 branding include a faith rally featuring mostly conservative Christian speakers, and multiple sports events, including a card of mixed martial arts bouts on the White House grounds for Trump's 80th birthday on June 14.
An IndyCar race in Washington is scheduled for August.
The Freedom 250 organisation also sponsored "Freedom Trucks" that critics say paint an overly religious version of American history and gloss over issues such as slavery and racial injustice.
A Reuters/Ipsos poll found that a majority of Americans, including three-quarters of Democrats and half of Republicans, think the events celebrating the country's 250th anniversary have grown too political.
Trump has sought to remake wide swathes of the capital city ahead of the 250th celebration, with mixed results.
Many fountains and statues have been renovated, but problems have beset a much-touted $15 million renovation of the Lincoln Memorial's Reflecting Pool.
Security cameras and soldiers now stand watch over its peeling paint and algae-fouled waters.
with Reuters
