In a dramatic state-of-the-nation speech earlier this month, Putin unveiled an array of new nuclear weapons that he said have no equal and would make US missile defence useless.
Putin won his fourth presidential term Sunday with almost 77 percent of the vote - his strongest electoral support ever.
He said the nation needs unity to move forward and urged the crowd to "think about the future of our great motherland".
While Putin has seven challengers on the ballot, none is a real threat.
Director of the Lenin State Farm Pavel Grudinin, nominated by the Communist Party of Russia, is second with 11.80% of the vote, while leader of the Liberal Democratic Party of Russia (LDPR) Vladimir Zhirinovsky is third with 5.66%.
Soini did not take a stand on whether some irregularities reported should be taken up with the Russians.
The residents of Moscow who chose to cast their votes for a presidential candidate and vote on the address of permanent residence registration may choose the most convenient polling station among 3,605 ones, only taking their passports along with.
Putin loyalists said the result was a vindication of his tough stance towards the West.
The overwhelming victory, however, has been overshadowed by widespread reports of vote rigging, and an election campaign in which, according to the Kremlin's critics, a genuine opposition was prevented from participating.
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Many countries around the world and in Europe did not realise how unsafe Hitler was until what happened, happened. The Saudi economy is larger than the Iranian economy. "What we did in Saudi Arabia was extremely necessary".
Navalny - who called on his supporters to boycott the "fake" vote and sent more than 33,000 observers across the country to see how official turnout figures differed from those of monitors - said there had been "unprecedented violations".
Ahead of the vote, a new crisis broke out with the West as Britain implicated Putin in the poisoning of former double agent Sergei Skripal with a Soviet-designed nerve agent.
Critics accuse him of overseeing a corrupt, authoritarian system and of illegally annexing Ukraine's Crimea region in 2014, a move that isolated Russian Federation internationally.
The 65-year-old president has made many such trips across the vast country, reaching out to various social groups and industrial sectors.
The Russian leader's popularity remains high despite his suppression of dissent and reproach from the West over Russia's increasingly aggressive stance in world affairs and alleged interference in the 2016 U.S. election.
Russian President and Presidential candidate Vladimir Putin delivers a speech during a rally and concert marking the fourth anniversary of Russia's annexation of the Crimea region, at Manezhnaya Square in central Moscow, Russia March 18, 2018.
Officials and analysts say there is little agreement among Putin's top policymakers on a new economic strategy. Ukraine is split between a volatile government in Kiev and a Russia-backed separatist region stuck in a frozen but still deadly conflict that serves Putin's interests.
Putin for longer also means stability in the corporate sector, a favourable outcome for bond investors.
The constitution limits the president to two successive terms, obliging him to step down at the end of his new mandate - as he did in 2008 after serving two four-year terms. But the President hasn't groomed a successor, prompting speculation he may try to find ways to extend his power beyond this term.
Mr. Putin's expected re-election means a continuation of the multi-faceted conflict between Russian Federation and the West, with an information war raging alongside real fights in Ukraine and Syria, and both sides seeking to damage the other's economy via sanctions.