In a speech on the eve of the vote, Tsipras also issued a strong call for "a better Europe, and a new and inspiring vision for Europe's citizens."
His message came when he addressed parliamentarians from the 47-nation Council of Europe in Strasbourg on Wednesday.
Europe faces a political and social crisis which is shaking it to its very foundations, he said.
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The economic crisis has "awakened the monster of populism" which is trampling on European values.
The solution is "a new social contract" which would strengthen democracy and combat inequality, he declared, citing the standards of the Council of Europe's revised social charter as a "sustainable common path for peoples and states."
He also spoke of Greece's huge efforts to deal with the humanitarian consequences of the migration and refugee crisis, and called on European partners to share the burden of dealing with the crisis on the basis of solidarity.
He praised the work of the Council of Europe, recalling its support for democracy in Greece during the dictatorship of the colonels in the 1970s.
In the British referendum, there will be no formal exit poll. Votes will be tallied by 382 local authorities (which range in number from 700,000 registered voters in Birmingham to as few as 1600 in the Isles of Scilly).
The biggest set of results is expected around 3am and a strong indication of the final result by 4.30 am. UK electoral commission Chair Jenny Watson will declare the final result in Manchester.
Meanwhile, the Parliamentary Assembly of the Council of Europe (PACE) says that the closure by the former Yugoslav Republic of Macedonia of its border with Greece and the imposition of the EU-Turkey agreement in the Aegean islands is "crushing Greece between two brutal realities."
It said that "the first victims of the situation in Greece are the refugees and migrants", of whom 46,000 individuals are blocked on the mainland and some 8500 on the Aegean islands.
At the same time, PACE said that Greece had been "left bearing a grotesquely disproportionate burden simply because of its place on the map", despite being "in every other respect perhaps the least well-placed of all EU countries to bear this responsibility."
PACE also accused Europe of making a "panicked response" to the refugee and migration crisis.
The assembly also called on Europe's governments to open all positions in the armed forces to women and to show "zero tolerance" to gender-based violence in the military.