Putin, aged 65, has been in power, eir as president or prime Minister, since 2000. Demonstrations took place in Moscow and several other cities across Russian Federation.
There have been fears of new unrest on Monday as he takes office. The economy has partially recovered from the depths of 2015-16 when the ruble lost half its value, but concerns persist about long-term prospects, especially if Russian Federation is unable to boost its manufacturing sector and wean the economy off its overwhelming dependence on oil and gas exports.
Mr Putin is only expected to meet volunteers who took part in his election campaign, the agency says.
Even if some of the demonstrations were not authorised in the location where they took place, this can not justify police brutality and mass arrests, European Union spokeswoman Maja Kocijancic said.
Putin won a landslide re-election victory in March, extending his grip over the world's largest country for another six years until 2024, making him the longest-lasting leader since Soviet dictator Josef Stalin who ruled for almost 30 years. Allegations of ballot-rigging had dogged previous elections too.
Police bundled away Alexei Navalny, the opposition leader, a few minutes after he arrived.
The arrest stemmed from the fact that Russian officials, who require applications be filed and approved for rallies, did not issue a permit to Navalny for the protest in Pushkinskaya Square.
Mr Putin's most praiseworthy achievement was restoring Russia's world status as a great power (47 per cent), according to the poll.
Could Putin just go on and on?
Putin circumvented the country's two-term limit in 2008, serving as prime minister but effectively retaining power as Medvedev served a four-year term as president.
The head of the Political Expert Group think tank in Moscow, Konstantin Kalachev, insisted that Mr Putin "serving another six years is a road to nowhere" as he forecast a "surprise" when the leader eventually hands over the reigns of Russian Federation leadership to a successor.
By the end of his new term, Putin will have ruled for 24 years.
The violence included a seeming throwback to an era of crowd-control tactics in Russian Federation.
When Grand Palace of Kremlin concludes inauguration ceremony, one of first acts of new president will be to propose his candidate for position of Prime minister, who will have to form new government.
Separatist violence in the North Caucasus which had plagued the administration of Mr Putin's predecessor, the late Boris Yeltsin, was finally brought to a bloody end. Backed by state television and ruling party, and credited with an approval rating of about 80%, his followers praise him as "far figure" of nation, which has restored national pride and expanded global influence of Moscow With interventions in Syria and Ukraine.
Putin's new term begins amid historically poor relations with the United States over efforts to interfere in the 2016 USA presidential elections, worldwide concern over Russia's human rights record and the lingering geopolitical fallout from the 2014 decision to secretly occupy and annex Crimea from Ukraine.
He explained: "Russia hasn't been so isolated since the Soviet war in Afghanistan".
He went on: "Now his task isn't to bring any new lands to Russian Federation, but to force the world to consider Russia's interests and accept its previous conquests".
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