Meanwhile, in east Ukraine, where pro-Moscow rebels plan a referendum on Sunday to follow Crimea in breaking away from Kiev, 20 pro-Russia rebels were reported killed on one of the bloodiest clashes yet in the port of Mariupol.
The head of Nato, locked in its gravest confrontation with Russia since the Cold War, condemned Mr Putin's visit to Crimea, whose annexation in March has not been recognised by Western powers. He also renewed doubts over an assurance troops has been pulled back from the Ukrainian border.
The government in Kiev called Mr Putin's visit, his first since the takeover of the region two months ago, a "provocation" that was intended to escalate the crisis.
Speaking at a concert during his first visit to Crimea since its annexation in March, Mr Putin said Russians' rights, including the right to self-determination, should be treated with respect.
"We treat all countries, all peoples, with respect. We respect their lawful rights and interests. But we ask that everybody should treat our lawful interests, including restoring historical justice and the right to self-determination, in the same way," he said.
Watching a military parade in Sevastopol on the Black Sea, Mr Putin said: "I am sure that 2014 will go into the annals of our whole country as the year when the nations living here firmly decided to be together with Russia, affirming fidelity to the historical truth and the memory of our ancestors.
"Much work lies ahead, but we will overcome all difficulties because we are together, which means we have become stronger."
Earlier in the day he had presided over the biggest Victory Day parade in Moscow for years. The passing tanks, aircraft and intercontinental ballistic missiles were a reminder to the world - and Russian voters - of Mr Putin's determination to revive Moscow's global power, 23 years after the Soviet collapse.
"The iron will of the Soviet people, their fearlessness and stamina saved Europe from slavery," Mr Putin said in a speech to the military and war veterans gathered on Red Square.
Speaking in formerly Soviet Estonia, Nato Secretary-General Anders Fogh Rasmussen said: "His visit to Crimea is inappropriate."
In Mariupol, Ukrainian forces drove pro-Russian rebels from police headquarters yesterday, killing 20 of them, the Kiev Interior Ministry said. The forces then withdrew from the centre of the city.
The action appeared to be one of the biggest yet in Kiev's attempt to end an insurgency in the country's east, though the number of dead could not be independently confirmed. Having expelled the armed fighters from the building, which was burnt out in the course of the clashes, the Ukrainian forces abandoned the area.
International efforts are afoot to forge some form of settlement in Ukraine to prevent a slide into a civil war that could have dramatic consequences for the whole region. With presidential elections approaching in two weeks, Kiev is under pressure to restore order across the country.
Interior Minister Arsen Avakov said an attempt by "terrorists" to seize the police headquarters turned into a pitched battle inside the building with Ukrainian army, national guard and security forces.
"A terrorist group of about 60 men armed with automatic weapons attacked the police headquarters ... about 20 terrorists were destroyed and four taken prisoner," Mr Avakov said on his Facebook page.
Ukrainian Prime Minister Arseny Yatseniuk, in office since an uprising overthrew the elected president in February, rejects Russian allegations that his power is the result of coup backed by neo-Nazi Ukrainian nationalists.
"69 years ago, we, together with Russia, fought against fascism and won," he said after a Victory Day church service in the capital. Now, he added, "history is repeating itself but in a different form".
In a dramatic and apparently conciliatory gesture, Mr Putin on Wednesday urged the Ukrainian separatists to call off the secession referendum they plan in the Russian-speaking regions of Donetsk and Luhansk. However, they plan to go ahead. Moscow insists it has no direct control over the armed militants, despite assertions to the contrary from Kiev.