He called up Mr Wickremesinghe to congratulate him on his victory in the Monday parliamentary polls that saw his United National Party (UNP) secure the maximum number of seats.
"The Secretary-General encouraged the Prime Minister and the national unity government to seize this opportunity to advance long-term peace for all Sri Lankans. He wished him success in the important task that lay before him," the UN said in a statement today.
The statement added that Mr Ban had a telephone conversation with Mr Wickremesinghe after the latter was sworn in at a ceremony yesterday in Colombo and praised his message of "good governance and national unity".
In a historic deal, the UNP has joined the opposition UPFA to form a government of national unity for a minimum period of two years.
Mr Wickremesinghe is expected to push ahead with his stalled reforms agenda in the country still grappling with challenges in the aftermath of the three-decade-long civil war with the LTTE.
Reconciliation and ethnic harmony are among the main pillars of the unity government structure as per an MoU entered between the two parties yesterday in an attempt to reach out to minorities, including Tamils.
The UN took a hands-on approach in Sri Lanka's separatist conflict since the military campaign ended in 2009 with the defeat of the LTTE.
Mr Ban visited Sri Lanka two days later and pressed for an investigation into civilian casualties in the final stages of the war. A UN internal probe on its role in Sri Lanka during the final stages of the conflict had ruled that the UN system had failed in the task of protecting the civilians.
Later, the UN Human Rights Council passed three successive resolutions against Sri Lanka's human rights accountability.
The last resolution in 2014 set up an international investigation into alleged war crimes by both government troops and the LTTE.
The UNHRC report is to be released next month after it was deferred from March as a goodwill gesture to the new government elected in January this year.
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