Voting ended at 6 p.m. local time (1600GMT) and turnout was 71.4 percent — well down on 2013’s high of over 80 percent.
A poll for Cybc put Anastasiades on between 38-42 percent with the nearest challenger, the communist-backed independent Stavros Malas on 27-31 percent.
An exit poll for state broadcaster RIK had Anastasiades on between 37.5-41 percent and Malas on 26-29.
Live results can be seen here (in Greek):
Anastasiades had gone into Sunday’s election as the favorite in a campaign dominated by the economy and stalled efforts to reunify the divided island.
Among the nine candidates for the top job — all male — the center-right Democratic Rally leader was projected to win the first round.
However, although Cyprus’ economy has improved since 2013, failed UN-backed peace talks over reuniting the island in July last year collapsed.
Almost 30 percent of the electorate refrained from taking part on Sunday, according to official Cypriot figures.
Tensions on the island persist. Recently a Turkish Cypriot newspaper was attacked by crowds after it drew the ire of Turkey’s leader, Recep Tayyip Erdogan, for coverage hostile to Turkey’s military operations in Syria.