"In his meetings, the deputy secretary-general stressed the need for calm and international unity in the pursuit of peace," Xinhua quoted UN spokesperson Martin Nesirky as saying.
At the request of UN Secretary General Ban Ki-moon, Eliasson on Sunday traveled to Ukraine to assess the situation on the ground. On Tuesday, he met with the acting president, prime minister and acting foreign minister.
Nesirky said that Eliasson reiterated Ban's call that Ukraine's territorial integrity should be respected and preserved.
Eliasson also held meetings with diplomatic representatives in Kiev and will continue his mission in Ukraine on Wednesday, the spokesperson noted.
Ban Ki Moon: Ukraine's territorial integrity should be respected and preserved
As part of the mission, Eliasson has asked UN Special Advisor Robert Serry, who has been in the region since last week, to travel to crisis-gripped Crimea in order to take stock of and evaluate the situation there," Nesirky said.
Serry is now departing Kiev and should arrive shortly in Crimea, the spokesperson added.
The Ukraine crisis, which originated from protests against President Viktor Yanukovych's decision last November to abandon an association agreement with the European Union and instead seek Russian aid, took an abrupt turn in the past two weeks following bloody clashes between protesters and police. Yanukovych then fled Kiev.
Last week, Ukraine's autonomous republic of Crimea became the new epicentre of an ongoing tension in the East European country, as armed groups seized government and parliament buildings in Crimea and took control of the two airports. Russian flags were raised over the seized buildings.
On Mar 1, Russia's upper house of the parliament approved President Vladimir Putin's request for using armed forces in Ukraine "in connection with the extraordinary situation and the threat to the lives of citizens of the Russian Federation."