Ottawa is under a state of emergency as police try to contain the protest.
Up to a quarter of so-called Freedom Convoy vehicles have children in them who could be at risk during operations, authorities said on Tuesday.
Nearly 80 criminal investigations have been opened relating to the protests.
Out of thousands of demonstrators, some two dozen arrests have been made.
While the protest has been mostly peaceful, police expressed concern about extremist rhetoric coming from far-right groups at the rally. As well as reported racial and homophobic abuse, protesters danced on the Tomb of the Unknown Soldier at the National War Memorial.
Officers have issued tickets and warned people away, but have been met by protesters determined to stay, and even a fake bomb threat which authorities said was intended to “deceive and distract” police.
One officer was reportedly attacked while attempting to seize fuel from a protest truck.
Speaking to press on Tuesday, deputy police chief Steve Bell said: “Our message to the demonstrators remains the same: Don’t come. If you do, there will be consequences.”
Incidents under police investigation include alleged hate crimes and property damage.
Mr Bell also disclosed on Tuesday that police had found about 100 trucks with children in them and contacted Children’s Aid Society overs concerns with noise, fumes and hygiene.
Some 740 miles (1,190km) away from Ottawa, Canada’s busiest border crossing was partially reopened on Tuesday after protesting truckers ground traffic to a standstill.
Truckers rallying in solidarity with those in Ottawa had blocked the Ambassador Bridge on Monday night, forcing vehicles to take long detours.
The bridge over the Detroit River is a vital trade link between Canada and the US, with more than 40,000 people and $323m (£238m) worth of goods cross it daily.
Sixty business groups from the US and Canada have called for an end to the blockade.
According to police in Michigan and Windsor, protesters had forced authorities to close the span shortly before 21:00 local time on Monday – just hours after Canadian Prime Minister Justin Trudeau had accused the demonstrators of attempting to “blockade our economy”.
Hundreds of vehicles were backed up for miles as travellers were warned by Canadian police to reroute.
While now open for travel from Canada to the US, across the other side, the Michigan Department of Transportation said the bridge remained closed and advised drivers to divert to nearby Port Huron to head into Canada. Business groups in the US and Canada called the blockade “an attack on the well-being of our citizens and the businesses that employ them”, and demanded a full reopening.
As traffic continued to clog the area, demonstrators in Ottawa faced anger from local residents even as many insisted that they were protesting peacefully.
“There’s been nothing but love, unity and peace out here,” said John Van Vleet, a trucker from Ontario. “It’s important for me to come down here to fight for my freedoms.”
However, some Ottawans have said the atmosphere has been tense, especially on weekends when thousands of protesters have descended upon the city’s downtown core, spilling into nearby streets.
“We’re all fed up,” said Marika Morris, a resident. “They don’t have a right to take us hostage.”
Ottawa has been under a state of emergency since Sunday.
Even before that, the city centre had been paralysed for a week as hundreds of lorries parked in the city centre and gatherings of protesters had forced businesses to close.
Residents’ nerves were also being frayed by constantly blaring air horns. On Monday, an Ottawa judge ruled that the truckers must stop honking their horns for 10 days.
The so-called Freedom Convoy began on 9 January in western Canada as truckers protested against a rule that requires them to be vaccinated against Covid-19 to cross the US-Canada border. The demonstrations have morphed to include anger at a raft of Covid-19 restrictions and at Mr Trudeau’s government generally. (Courtesy BBC)