AI research firm Transluce said the attempts exhibited tactics "consistent with prior observed agent activity that we have attributed to OpenAI in a similar time frame".
But it said it was not confidently attributing these attempts to OpenAI.
The agents attempted to access Library and Archives Canada on May 28 and June 9, Transluce said in a blog post.
Transluce said it disclosed the action to the Canadian government on Monday.
The Canadian Centre for Cyber Security said on Tuesday it was aware of reports of suspected AI agent activity.
"There is no indication that government systems have been compromised at this time," it said in a statement.
"We do not confidently attribute these attempts to OpenAI, but they exhibit tactics consistent with prior observed agent activity that we have attributed to OpenAI in a similar time frame."
OpenAI said it was "aware of reports of OpenAI models attempting to access publicly available information from Canadian government websites".
A spokesperson said OpenAI was reviewing the reported findings and had provided an initial briefing to Canadian officials conducting the government's review.
The world's leading AI companies have warned of the risks posed by AI to humanity, appealing for governments to work together to manage the increasingly powerful technology.
Several recent breaches globally by rogue AI agents have alarmed governments and companies.
Last week, Australia said an OpenAI agent breached a government health data portal in June, gaining unauthorised access to files, in what was the first known instance of an AI agent hacking into a government website.
OpenAI apologised on Tuesday for the hacking of the Australian government website by the rogue AI agent.
