"Advocating the violent overthrow of a sovereign state is unacceptable," Straw said in a statement on Tuesday.
Straw said that Berezovsky's residence status could be reviewed if his presence was not "conducive to the public good".
In an interview with Reuters earlier this month, Berezovsky said he was "preparing a forced takeover of power in Russia".
In his statement, Straw pointed to comments Berezovsky made in another interview last month and said he condemned Berezovsky's remarks "unreservedly".
"The UK government will take action against those who use the UK as a base from which to foment violent disorder or terrorism in other countries," Straw said.
Berezovsky, once one of Russia's richest men and a senior official in the 1990s under then President Boris Yeltsin, has been a vocal opponent of Putin since moving to London in 2000 shortly after Putin took power in Moscow.
"The UK government will take action against those who use the UK as a base from which to foment violent disorder or terrorism in other countries"
British Foreign Minister
He accused Putin of creating an over-centralised and weak regime and said "coercive actions to take power" were justified if they were taken to restore Russia's constitution.
He said on Tuesday he had read Straw's statement and was preparing a written response.
"I want the minister to receive information from me and not through the media," Berezovsky said, declining further comment.
Britain damaged cordial relations with Russia when it granted Berezovsky asylum status in 2003.
London has refused to return the former oligarch to Russia to stand trial on fraud charges, which Berezovsky calls politically motivated.
Berezovsky controlled much of Russian media during the Yeltsin years and has claimed he helped engineer Putin's rise to power, but quickly fell out with the new president and became an outspoken critic from London.
Straw's warning to Berezovsky comes after a period of mounting tension with Russia.
"I want the minister to receive information from me and not through the media"
Moscow last month accused London of running a James Bond-style spying operation in the Russian capital using a receiver hidden in a fake rock to gather secret information.
Moscow named four British Embassy workers as intelligence officers running Russian agents, and accused the embassy of funding Russian human rights groups.
Britain says its funding of Russian civic groups is legitimate and open.