Vladimir Putin has written a letter telling Boris Nemtsov’s mother, Dina Eidman that he 'shares her sorrow.'
The message of condolences from the President, published on the Kremlin website, reads in part:
Please accept my deepest condolences in connection with this irreparable loss. I sincerely share your sorrow.
Boris Nemtsov has left his mark in the history of Russia, in its political and public life. He occupied significant posts in a difficult time of transition in this country. He always openly and honestly voiced and upheld his views.
We will do everything to ensure that the perpetrators of this foul and cynical crime and those who stand behind them are properly punished.
Russian president Vladimir Putin says a ceasefire in the Ukraine conflict has been agreed.
The ceasefire will begin on Sunday, he said and heavy artillery will be removed.
Speaking to reporters after almost 16 hours of talks, Putin said: "We have managed to agree on the main issues."
Russian President Vladimir Putin will take part in the Minsk talks on the situation in eastern Ukraine, Interfax news agency reports, citing a Kremlin spokesperson.
The White House said President Barack Obama urged Russian President Vladimir Putin in a phone call to agree to a peace deal.
"If Russia continues its aggressive actions in Ukraine, including by sending troops, weapons, and financing to support the separatists, the costs for Russia will rise," the White House statement added.
The Kremlin, in its statement about the call, said Putin and Obama highlighted the need for the need for a political solution to the "internal" conflict in Ukraine.
The Kremlin also said the two leaders also noted the necessity to safeguard the rights of inhabitants of all Ukrainian regions, including Russian-speakers in the east.
Foreign Secretary Philip Hammond has accused Russian President Vladimir Putin of acting like a "mid-20th century tyrant" over Ukraine,
Mr Hammond said that President Putin reverse its annexation of the Crimea and start respecting international law.
He also predicted that Russian economic decline - partly as a result of international sanctions - would curb its "outrageous" foreign adventures.
A claim that Russian President Vladimir Putin has Asperger's syndrome is "stupidity not worthy of comment," a Kremlin spokesman said.
Dmitry Peskov's comment to the Gazeta.ru website comes after it was revealed that a Pentagon report, written in 2008, theorised the Russian president has "an autistic disorder which affects all of his decisions".
The study, conducted for Pentagon thinktank the Office of Net Assessment, monitored Putin's movements and concluded that in very early life he "suffered a huge hemispheric event".
White House spokesman Josh Earnest said he had no comment on the report.
People in the Russian capital of Moscow have been seen celebrating president Vladimir Putin's 62nd birthday today.
A huge banner hung from a bridge in the city showing US president Barack Obama wearing a T-shirt wishing happy birthday to 'global daddy' Putin.
Shops in the capital sold T-shirts and sweatshirts emblazoned with their leader's face.
But demonstrators in Poland chose today to protest against Putin's rule outside the Russian embassy in Warsaw.
A deal to end fighting in eastern Ukraine could be reached this week, Russian President Vladimir Putin has said.
Following a phone call with Ukrainian President Petro Poroshenko, Putin said their views on ending the violence were "very close" and suggested Kiev and the pro-Russian separatists could reach an agreement by Friday.
Earlier US President Barack Obama said a ceasefire would only succeed if Russia stopped sending troops "disguised as separatists" into Ukraine.
Russian President Vladimir Putin and his Ukrainian counterpart Petro Poroshenko have spoken by phone and "largely agree" on a possible way out of the Ukraine crisis, Interfax news agency reported, citing Putin's spokesman.
"The viewpoints of the presidents of the two countries largely coincide on possible ways out of the grave crisis situation," Dmitry Peskov was quoted as saying.
President Vladimir Putin said Moscow could not stand aside when people were being shot at in Ukraine, he told Russia's state TV Channel 1 in an interview.
It must be borne in mind that Russia cannot stand aside when people are being shot at almost at point blank.
Mr Putin also said ending the crisis was down to "the political will of the current Ukrainian authorities".
The West has accused Moscow of supporting pro-Russian separatists who are fighting Ukrainian government forces in the east of the country.