Mr Tsipras' Syriza bloc is predicted to come first in new elections called for 17 June. Syriza wants to renegotiate Greece's international bailout.
At least 700m euros (£560m; $890m) was withdrawn from Greek banks in the week until Monday, the Greek president said.
But there are no signs of a bank run.
'Poverty and hardship'
In a BBC interview, Mr Tsipras said if the "disease of austerity destroys Greece, it will spread to the rest of Europe".
Banks were profiting at the expense of thousands of Europeans - in Spain and Italy, as well as Greece - left in poverty and hardship, he said.
"Therefore the European leadership and especially Mrs Merkel need to stop playing poker with the lives of people," Mr Tsipras said.
Syriza came second in inconclusive elections on 6 May, in which no party won a majority or was able to form a coalition.
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