The Chancellor also denied the Kremlin is “laughing at us” over Britain’s response to the killing and the suspicion that Russia was also involved in the poisoning of double agent Sergie Skripal.
But Mr Hammond insisted there were “very strict rules” surrounding donations, which could only come from British citizens and were “carefully vetted”.
“There are people in this country who are British citizens who are of Russian origin. I don’t think we should taint them, or should tar them with Putin’s brush,” he said.
Speaking on the BBC’s Andrew Marr programme, Ms Litvinenko said the prime Minister had broken her pledge – in a personal letter she brandished – to do everything to prevent a repeat of her husband’s murder.
But the Chancellor insisted: “Nobody is laughing at us. This is a very serious investigation that is going on, let’s see where it leads us.”
The Sunday Times reported that Russian oligarchs and their associates have registered donations of more than £820,000 to the Tories since the summer of 2016.
Ms May promised to distance her party from Russian donors when she took office, her allies briefing that she would “sup with a long spoon” and reject a “business-as-usual” relationship with Moscow.
The Tories have received more than £3m from Russian billionaires and lobbyists for Moscow since their return to government in 2010.
And one of the most controversial donors paid the party more in a year under Ms May than in six years under David Cameron, the paper reported.
Lubov Chernukhin, the wife of a former Putin minister, handed the party £253,950 in the year to September 2017, Electoral Commission figures show, and bid £30,000 to have dinner with Gavin Williamson, the Defence Secretary.
In her interview, Ms Litvinenko warned the lesson “was not learned”, more than a decade after her husband, an outspoken critic of Vladimir Putin, was fatally poisoned.
A public inquiry concluded in 2016 that the killing of the Russian dissident had “probably” been carried out with the approval of the Russian president.
Ms Litvinenko was speaking as Mr Skripal, 66, and his 33-year-old daughter Yulia remain in hospital following the suspected nerve agent attack in Salisbury a week ago.
Detectives have yet to identify who was responsible, but Foreign Secretary Boris Johnson triggered a diplomatic row by pointing the figure at the Kremlin – something rejected by the Russian Embassy.
Ms Litvinenko showed a letter, sent to her by Ms May, when Home Secretary, promising to “continue to pursue justice” over the murder, to ensure no repeat.
But she said: “Unfortunately it happened again and the lesson after the murder of my husband was not learned.
“We understand the relationship between two countries such as Russia and the UK need to be at a high level.
“But we know Russia never supported the investigation into the killing of my husband, nobody was punished and people who were the killers of my husband were not even suspects.”