"This is a police investigation and it will be evidence-led and we must go where the evidence takes us," Hammond told BBC television.
"So we have to allow the police investigation to run its course. But if there were to be an involvement of a foreign state evidenced by this investigation, then obviously that would be very serious indeed and the government would respond appropriately," he said.
British police have identified more than 200 witnesses and are looking at more than 240 pieces of evidence in their investigation into a nerve agent attack on a Russian ex-spy and his daughter, interior minister Amber Rudd said on Saturday.
Former double agent Sergei Skripal, 66, and his daughter Yulia, 33, have been in hospital in a critical condition since Sunday, when they were found unconscious on a bench in the southern English cathedral city of Salisbury.
Skripal betrayed dozens of Russian agents to British intelligence before his arrest in Moscow in 2004. He was sentenced to 13 years in prison in 2006, and in 2010 was given refuge in Britain after being exchanged for Russian spies.
Many in British media and politics have speculated that Russia could have played a part in the attack, but the Kremlin has denied any involvement in the incident and accused the British media of whipping up anti-Russian hysteria.
Traces of a nerve agent used in the suspected attempted murder have been found in a pub and a restaurant he visited, England's chief medical officer said Sunday.
Sally Davies said up to 500 people who had visited The Mill pub and the Zizzi restaurant in Salisbury, southwest England, needed to wash their clothes and belongings as a precaution.