Tony Blair and Russian President Vladimir Putin have pledged to increase their countries' joint efforts to combat terrorism.
Vladimir Putin is on the second day of his visit to the UK
The states plan to boost co-operation to "counter this scourge", they said on their second day of talks in London.
Mr Putin visited the Cobra briefing room where the government plans its emergency response to terror attacks.
Trade was also set to be on the agenda, with Mr Blair saying the two countries' economic futures are bound together.
Mr Putin presented awards to the British crew who took part in the rescue effort in August to save a team of Russians trapped in a submarine.
Mr Putin is the first foreign leader to see the high-security Cobra room, where their talks took place.
The two leaders said their countries have "suffered at first hand the cruelty and inhumanity of terrorism", in a statement after their meeting.
It continued: "Today, we reaffirm our utter condemnation of terrorism in all its forms and our determination to strengthen existing co-operation to counter this scourge."
Mr Blair's recent focus on new anti-terrorism laws matches Mr Putin's conviction that more needs to be done to counter international terrorism, the BBC diplomatic correspondent Bridget Kendall says.
It is more than two years since President Putin last visited Downing Street.
Since then there has been a chill in relations between the UK and Russia, our correspondent says.
The Kremlin reacted angrily when British courts refused Russia's request to extradite two outspoken critics of the Russian government, the prominent Chechen separatist, Ahmed Zakayev and wealthy Russian businessman Boris Berezovsky, before granting them political asylum.
But now it seems as if both sides want to put aside their differences, our correspondent says.
The Downing Street summit comes the day after Mr Putin met Mr Blair and other European Union leaders for talks which focused on plans for increased supplies to Europe of Russian oil and gas.
Soon Russia is expected to be supplying 50% of the EU's natural gas needs.
"We want to work to take the relationship between Europe and Russia to a new and more intense and strengthened level," Mr Blair said.