OTTAWA (Reuters) - Canada will continue to accept asylum seekers crossing illegally from the United States but will ensure security measures are taken to keep Canadians safe, Canadian Prime Minister Justin Trudeau said on Tuesday.

The number of would-be refugees crossing into Canada at isolated and unguarded border crossings has increased in recent weeks amid fears that U.S. President Donald Trump will crack down on illegal immigrants, and photos of smiling Canadian police greeting the migrants have gone viral.

Opposition Conservatives want Trudeau's center-left Liberal government to stem the flow of asylum seekers from the United States because of security fears and a lack of resources to deal with them.

"One of the reasons why Canada remains an open country is Canadians trust our immigration system and the integrity of our borders and the help we provide people who are looking for safety," Trudeau told parliament.

"We will continue to strike that balance between a rigorous system and accepting people who need help."

Immigration Minister Ahmed Hussen also said Canada would continue to honor the Canada-U.S. Safe Third Country Agreement, which requires it to turn back refugees if they make asylum claims at Canadian border crossings with the United States. Refugee advocates have argued this drives asylum seekers to cross illegally at isolated locations, risking their lives in frigid weather.

Amnesty International and other groups are pressuring the Canadian government to abandon the agreement, arguing the United States is not safe for refugees.

Canadian police said on Monday they had bolstered their presence at the Quebec border and that border authorities had created a temporary refugee center to process the asylum seekers.

The number of people making refugee claims at Quebec-U.S. border crossings more than doubled from 2015 to 2016. Last month, 452 people made claims in Quebec compared with 137 in January 2016.

The influx is straining resources in the western prairie province of Manitoba and in Quebec, where taxis drop asylum seekers off meters away from the Quebec-U.S.border, the Canada Border Services Agency (CBSA) said.

The right-leaning Conservative opposition have called on Canadian authorities to hand illegal immigrants over to U.S. authorities, but Hussen said Canada can honor its refugee agreement with the United States while helping asylum seekers who enter the country illegally.

(Reporting by Andrea Hopkins; Editing by Cynthia Osterman)