U.S. President Donald Trump has offered to help Russia after a laboratory worker died following an illness at a plague research institute in Siberia, while the Russian authorities said the situation was under control.

"We'll help," Trump told reporters at the White House on Monday when asked about the case. "Everybody who has that kind of a problem, we'll always help," according to a Reuters transcript.

A laboratory worker at an anti-plague research institute in the Irkutsk region of eastern Siberia fell ill and died in undisclosed circumstances, reportedly prompting authorities to quarantine nearly 200 people and fueling public health concerns.

Trump said he had not spoken to Russian officials about the case, but described the plague as a "rough disease."

"That's a disease we used to be able to control," Trump said, adding that "somehow those microbes have gotten stronger and stronger, they're like an army."

"We are monitoring the situation closely with the CDC and our other interagency partners. Many details have not been confirmed. We encourage Russian authorities to share accurate information quickly and openly," a state department spokesperson who did not wish to be identified told CNBC.

Trump said the U.S. would do what it could to help Russia. He has previously said he considers Russian President Vladimir Putin someone he can work with, despite tensions over Moscow's war in Ukraine.

The World Health Organization in an email response said the cause of death had not been confirmed and testing was underway. It said it was in contact with Russian authorities, and has offered support if needed, while assessing the risk to the general public as low based on available information.

It remains unclear whether Moscow has sought or would accept any assistance.