"We are committed to doing all we can to bring the perpetrators to justice, whoever they are and wherever they may be," she told MPs, describing it as a "brazen and reckless act".
"The investigation is moving at pace, and this government will act without hesitation as the facts become clearer," she said, adding: "We will respond in a robust and appropriate manner once we ascertain who was responsible."
In an update to the House of Commons, Rudd said Sergei Skripal and his daughter Yulia remained "unconscious and in a critical but stable condition" after being found collapsed on a bench in the southwestern English city of Salisbury on Sunday.
A police officer who attended the scene "remains serious but stable and is conscious, talking and engaging", she added.
Police confirmed late Wednesday that Skripal and his daughter were attacked by a nerve agent, and Rudd said it was "highly likely" the police officer was also exposed.
She refused to speculate further on the nature of the agent or who was responsible while the police continued their complex and fast-paced investigation.
But Rudd warned it was a "most outrageous crime", adding: "The use of a nerve agent on UK soil is a brazen and reckless act.
"This was attempted murder in the most cruel and public way. People are right to want to know who to hold to account."
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