Police confirmed Wednesday that a nerve agent was used in the attack in the southern English city of Salisbury on Sergei Skripal and his daughter, Yulia, who remain in a critical but stable condition.
In a statement to members of Parliament on Thursday, Rudd refused to be drawn on who might have been responsible.
"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," Rudd said.
"People are right to want to know who to hold to account but if we are to be rigorous in this investigation we must avoid speculation and allow the police to carry on their investigation."
Rudd said the UK government was committed to "doing whatever we can to bring the perpetrators to justice" and would "act without hesitation as the facts become clearer."
A split image showing former Russian spy Sergei Skripal and his daughter, Yulia Skripal.
Skripal, 66, and Yulia, 33, were found slumped on a bench near a shopping center in Salisbury on Sunday. A police officer who helped them was also exposed to the nerve agent but his condition has improved.
Earlier Thursday, Rudd said that Skripal and his daughter were in a "very serious condition" but that the policeman was "talking and engaging."
Police: Pair 'deliberately targeted'
In a statement on Wednesday evening Mark Rowley, the head of the counter-terrorism division at London's Metropolitan police, declared a "major incident" and said hundreds of police officers, forensic experts and government chemical analysts were involved in the inquiry.
Rowley said the attack was being treated as attempted murder, and that Skripal and his daughter were deliberately targeted.
If a Moscow link were proved, it would plunge relations between the West and Russia to a new low, and would call into question the British government's ability to protect residents of the UK at home. Rowley said officers from Wiltshire police, the local force, were providing support to the sick officer and his family.
Sally Davies, the Chief Medical Officer for England, said the evidence did not suggest any wider danger to the public.
