OTTAWA (Reuters) - The Canadian government is weighing the chances of a potential surge in asylum seekers illegally crossing into Canada from the United States as the weather improves, a government minister said on Tuesday.

RCMPofficers speak with a man before he crosses the U.S.-Canada border into Hemmingford, Quebec. REUTERS/Dario Ayala

Hundreds of people, mainly from Africa and the Middle East, have braved wintry conditions to cross into Canada, where they face arrest. The migrants and refugee agencies cite U.S. President Donald Trump’s crackdown on immigration as a reason for fleeing.

Border guards and police briefed cabinet on various scenarios on Tuesday. Ottawa has not decided what to do, Public Safety Minister Ralph Goodale told reporters.

Asked whether the government was looking at a scenario of a larger influx as the weather improved, Goodale replied: “That would be one of the considerations.”

Canadian officials - who have consistently said they are not worried by the numbers so far - stress it is too early to say whether the influx represents a trend.

“We’re obviously watching this very closely,” said Goodale.

U.S. Homeland Security Secretary John Kelly is scheduled to visit Ottawa on Friday for talks on the border and the influx, said Canadian officials.

“It’s important for them (the Americans) to understand the impact of this flow on Canada,” said Goodale.

Although the migrants link their actions to Trump’s policies, Canadian officials say the numbers started to rise before the U.S. presidential election in November.

Officials say virtually all of the people seeking asylum in Canada had been in the United States legally. Under the terms of a bilateral deal on refugees, Canada is obliged to reject bids by people who have already sought asylum in the United States.

“Some of these individuals who are coming across our borders never intended to stay in the United States ... Canada for them was always the destination,” Immigration Minister Ahmed Hussen told reporters.

Canadian officials discovered many people entering Quebec province obtained visas from the U.S. Embassy in Riyadh, said one person familiar with the matter.

Separately, a senior political source said asylum seekers were happy for now to give themselves up to police and escape the cold.

“What’s going to happen when the weather warms up? Are we really going to have to build a fence along the entire length of the border?” said the source, who asked to remain anonymous.

Such an undertaking would be impossible, since the frontier stretches 5,500 miles (8,900 km) and is largely unguarded.