He said the British were insulting themselves by forgetting they are no longer a colonial power.
"It's their mindset, not our constitution, which needs to be changed. What they are offering to us is a clear remnant of colonial thinking," Putin said on Tuesday.
"They need to treat their partners with respect, then we will show respect to them."
The office of Gordon Brown, the British prime minister, had no immediate comment on Putin's remarks.
The UK has rejected Russia's offer to try Lugovoi in Moscow, saying it was not an option for British prosecutors.
A British foreign office spokesman, however, said the government will continue to persuade Moscow to "work constructively with us" to try Lugovoi in a UK court.
Lugovoi is one of three Russians who met Litvinenko in a London hotel on November 1, 2007, the day he fell ill after ingesting radioactive polonium-210.
Before he died in a London hospital, Litvinenko accused Putin of being behind his poisoning, a charge the Kremlin has denied.
Alexander Zvyagintsev, Russia's deputy prosecutor general said on Monday that Russian investigators were working on "all versions" including "evidence that people from Litvinenko's close circle in London might have been involved in the crime".
|Zvyagintsev said prosecutors were investigating|
Litvinenko's close allies in London [Reuters]
The standoff escalated last week after Britain responded to Russia's refusal to extradite Lugovoi by announcing the expulsion of four Russian diplomats.
Russia countered by announcing that it would expel four British diplomats.
Expressing his irritation, Putin said Britain has refused to extradite several Kremlin critics including "30 people wanted by our law enforcement agencies for committing grave crimes".
"They didn't even sneeze, they didn't even think about extraditing them," he said.
"They don't extradite anyone, including those who are suspected of terrorist activities," added Putin. "At the same time, they are putting excessive demands to us."