Kingsley Amaning, the UN humanitarian co-ordinator in Chad who issued the statement, said they were "protesting the deteriorating security in eastern Chad and to reiterate our solidarity with the families and colleagues of all victims of this insecurity".
Representatives from UN agencies, NGOS, the Red Cross, donors and diplomats met late on Thursday in Chad and "expressed their solidarity" with Marlinge's friends and family, the UN statement said.
European peacekeeping forces patrolling the volatile region bordering Sudan's Darfur arrived at the scene shortly afterwards and set off to try and catch the killers, Jean Axelos, an officer with the force, told the AFP.
Marlinge left behind a wife and a teenage daughter, both living in France.
Save the Children has suspended all work in Chad until further notice and has sent a team to assist in the investigation.
A force of 3,700 European Union troops is due to be fully operational by the end of June in Chad and the Central African Republic in a region where hundreds of thousands of people have been displaced by conflict.
A spokesman for the European Union military force (EUFOR) in Chad said they did not have enough troops to escort humanitarian convoys in the conflict-torn eastern region where Marlinge was killed.
"If you take a map and look at the distances, it's clear that EUFOR can never be everywhere, all the time," said Jean Axelos.
Thursday's killing raised questions about the ability of the thinly stretched EU force, which is still deploying, to carry out its mandate to protect civilians, refugees and aid workers in an area of several hundred thousand square miles.
EUFOR has just over 2,200 troops deployed at the moment in east Chad.
The region has been racked by violence in recent years, including rebel offensives, inter-ethnic clashes and attacks by raiders coming over the border from war-torn Darfur.
Axelos said the European troops were concentrating on guarding refugee camps, humanitarian installations and store depots.