Anastasiades secured 45.4 percent of the vote and remains a favourite to clinch victory in the run-off.
This will come next Sunday when he goes head-to-head with communist-backed Stavros Malas.
Both must woo voters who backed a third man, George Lillikas, an independent deeply suspicious of any terms for a bailout.
Cyprus sought financial help last year after its banks suffered huge losses from Greece's sovereign debt restructuring.
The island needs about 17 billion euros in aid, roughly the equivalent of its GDP.
The Euronews correspondent in Cyprus says "In the six intervening days before the ballot boxes open again, the two remaining contenders for the presidency will try to win over not only as many as possible who supported the other candidates in round one, but also those who chose to abstain."
Source: Euronews
