Christofias' victory in replacing Tassos Papadopolous, his hardline predecessor, had raised hopes of a new drive to end the island's 34-year-old division.
Papadopoulos had led Greek Cypriots in rejecting a UN reunification plan in a 2004 referendum and talks went nowhere during his term of office.
Christofias was elected on a platform of intensifying negotiations with the Turkish Cypriots and had vowed since taking office last week to meet Talat as soon as possible.
Aides to the two leaders met earlier on Wednesday to discuss the date for the talks.
Moller, UN special representative for Cyprus, said: "The meeting took place in a very cordial and constructive atmosphere and the aides to the two leaders reached a great degree of convergence on the issues discussed, including on the possible future opening of the Ledra Street crossing."
Ledra Street, known as "Murder Mile" to British troops in the 1950s who fought with EOKA fighters seeking union with Greece, runs through the heart of the world's last divided capital.
A main commercial thoroughfare of the city, it is currently blocked in the middle by the UN-patrolled Green Line that divides the island.
Talat heads the self-declared Turkish Republic of Northern Cyprus (TRNC), announced in 1983 and recognised only by Ankara.
Greek Cypriot rejection of the 2004 reunification plan, which was overwhelmingly approved by Turkish Cypriots, meant that a divided island joined the European Union that year.
Cyprus has been split along ethnic lines since 1974 when Turkish troops occupied its northern third in response to a Greek Cypriot coup seeking union with Greece.
Christofias has said he hoped to be able to announce the opening of two more crossing points on the UN-patrolled Green Line, to supplement five currently in operation.
But the Cypriot president warned against expecting too much from the meeting with Talat, who is still backing a 2004 UN plan for the future of the island.
Christofias said he was only willing to resume talks with the UN as mediator along the lines of a stalled July 2006 agreement between the two sides.
This provided for co-operation on some specific matters like fighting crime while continuing to discuss power-sharing and territorial matters.
Christofias has said he is ready to accept the possibility of a federation on condition that Turkish troops leave the north of the island.