"The will of the Gambian people, freely expressed in exercise of their franchise, must be respected by all without precondition", said Liberia's President Ellen Johnson Sirleaf, who now chairs the West African regional bloc ECOWAS.
A later media statement issued by his party, the Alliance for Patriotic Reorientation and Construction (APRC) said he was challenging the results at the Supreme Court of the Gambia.
The delegation would "ask him to leave power", a source at the Senegalese foreign affairs spokesman said.
It further called on Jammeh to respect the ECOWAS Protocol on Democracy and Good Governance and the African Charter on Democracy, Elections and Governance, notably the rejection of unconstitutional change of government.
President Jammeh who has ruled The Gambia for over 22 years has annulled the elections and called for a re-run after earlier conceding defeat in Presidential polls.
Barrow has urged Jammeh to meet the heads of state when they arrive but could not confirm that the longtime leader would be present, saying that he had not spoken to him since December 2.
The Security Council "urged President Jammeh to meet and cooperate" with the high level delegation, said Deputy Spanish U.N. Ambassador Juan Manuel Gonzalez de Linares Palou. The Gambia Bar Association notes with concern that since May 2015 there has not been a sitting supreme court session due to the absence of a panel.
The members of the Security Council commended the people of the Islamic Republic of The Gambia for the peaceful and transparent holding of elections on 1 December 2016.
The Bar Association said there was "no legitimate legal mechanism available in The Gambia to hear and determine the election petition", as he would have to stuff the court with his own appointees.
"We don't have time to fight again".
A readjustment of the votes counted in the election was made on Monday, reducing numbers of ballots for all three candidates but ultimately confirming Barrow's victory.
However, after he declared a week later that the vote was "fraudulent and unacceptable" and "the most devious election we have ever had", and vowing to take the matter to the country's supreme court, Barrow and his coalition said Jammeh should resign now.