Anti-Kremlin activists urged ordinary Russians to join them on a memorial march through central Moscow, with other commemorative events planned across the country and abroad.
Before the start of the march Russians brought flowers and candles to the bridge near the Kremlin walls where Nemtsov, a jovial 55-year-old with a mop of black curly hair, was killed.
US ambassador John Tefft was among those who came to pay respects, laying a wreath with a ribbon saying "From the American people."
Authorities allowed the opposition to hold a march through the city centre but forbade activists from marching to the bridge where Nemtsov's allies have struggled to maintain a makeshift shrine.
"The march in Nemtsov's memory is also a march demanding a normal country and normal state where contract killings in the form similar to public executions do not take place," wrote top opposition leader Alexei Navalny.
Putin, whose rule has seen the steady suppression of independent media and opposition parties since he came to power in 2000, branded the killing a "provocation" and promised an all-out effort to catch the killers.
"Who dared?" a furious Putin asked his aides after Nemtsov was hit in the back by four fatal shots, the country's top opposition Novaya Gazeta reported this week.
The five detainees - including Zaur Dadayev, a member of a Chechen interior ministry battalion accused of being the gunman - are now awaiting trial for what investigators say was a contract killing carefully planned over months.
But Nemtsov's family and allies insist the authorities have failed to bring the masterminds to justice and point the finger of blame at Chechnya's Moscow-backed strongman Ramzan Kadyrov - and the Kremlin itself.
