Canadian officials say it is too early to say whether a jump in illegal border crossings is part of a longer-term trend.
They also say they are not certain more border jumpers will come when the weather warms up.
Illegal crossings by asylum seekers have increased in the past few months across three provinces.
Prime Minister Justin Trudeau has been under pressure to do more to secure the border amid concerns about the influx.
Last year, the number of refugee claims rose steadily, but federal officials in a news briefing on Thursday warned the number of asylum claims can fluctuate significantly year-to-year.
The Royal Canadian Mounted Police (RCMP) confirmed there has been a specific increase in illegal migration over the past few months, with the largest jump being seen in the province of Quebec.
Between 1 January and 21 February this year, 290 people were intercepted crossing illegally in Quebec, 94 in Manitoba, and 51 in British Columbia, officials said during a news briefing on Thursday.
Those numbers do not include people who were not apprehended at the border and made their own way to inland border offices to make a claim.
Of those who have crossed the border illegally seeking asylum, some have spent only a short time in the United States while others have pending or refused asylum claims south of the border, said the officials, who spoke to the media on background.
In Montreal in February, the RCMP hosted a meeting to discuss what it calls "irregular migration".
The RCMP, which is responsible for policing the Canada-US border between official crossings, is working closely with Canadian and US partners to "determine the extent of this complex issue", RCMP spokeswoman Annie Delisle told the BBC in an email.
At the Montreal meeting were representatives from the federal departments of Justice and Immigration, the Canada Border Services Agency, Quebec provincial police, and the Public Prosecution Service of Canada.
US Customs and Border Protection and US Homeland Security Investigations representatives were present from south of the border.
US Homeland Security Secretary John Kelly plans to travel to Ottawa soon to meet with his Canadian counterpart, Public Safety Minister Ralph Goodale, a representative for Mr Kelly said.
In recent years the number of asylum seekers crossing illegally has been creeping up steadily. But towns like Emerson, Manitoba have seen groups of 20 or more crossing in one night in this winter, overwhelming the municipality's resources and local settlement agencies.
On Thursday, asked by a reporter about the border jumpers, Mr Trudeau gave a "shout out" to first responders in towns like Emerson and in Quebec for their handling of the influx and said the federal government is continuing to monitor the situation.