The federal government is going to look at doing more to help Quebec deal with the flood of asylum seekers.

Quebec's Immigration Minister met his federal counterpart on Wednesday evening to discuss the influx of people crossing the border and asking to remain in Canada.

"We have the majority of asylum seekers come through Quebec and so we see here today that we've been proposing solutions and tonight there was a real openness for solutions," said David Heurtel.

Tens of thousands of people crossed the border last year outside of a border crossing station in order to seek asylum.

According to the Safe Third Country Agreement between Canada and the U.S. anyone seeking asylum at a border crossing between the two countries is refused and sent back to the other country to make their claim, but those who do so elsewhere are allowed to make their claim in the country where they are located.

So far in 2018, more than 6,000 people have crossed the border to make asylum claims, with most people doing so from Vermont into Quebec, where the border is easily accessible.

"People have to realize now in Ottawa that our system is stretched, and it cannot be stretched much more," said Premier Philippe Couillard.

Once people make a claim they are housed until dates can be set for an Immigration Hearing, but the massive increase in applicants in recent years has caused a backlog.

It's also been a large expenditure by the province for what is supposed to be a federal jurisdiction.

Quebec has asked Ottawa to provide $146 million to compensate the province for what it spent last year to deal with 25,000 asylum seekers.

Federal Transport Minister Marc Garneau said that, like last year, a triage system could be set up near the Lacolle border crossing to deal with migrants.

"We'll ask basic questions such as where do you really want to go in Canada. And if you're going to make your life here, where is it that you really want to go? Some of them don't necessarily all want to head to Montreal," said Garneau.

Currently people who are arrested near the border are brought to Montreal, then processed at the Immigration office in downtown Montreal.

"We have manpower shortages, labour shortages across Quebec, so with this triage if we can get them to work all of the measures will lessen the pressure on Montreal, because in Montreal the resources are saturated," said Heurtel.

In many cases those seeking asylum have contacts in Canada and move to another province once they are freed by Immigration and have their dates arranged for future hearings.

"A lot has happened in 2017, but the relationship is one of collaboration and it allows us to work together and there's no way we could have handled the situation better last year had it not been for amazing relationship we had with Quebec," said federal immigration minister Ahmed Hussen.

Both governments say they are committed to taking action as quickly as possible.