Nigeria's Super Eagles were forced to a 2-2 draw at home by Tunisia on Sunday to remain in second place in Group 2, two points behind leaders Tunisia. Only the winners will qualify for the finals in South Africa.
Top government officials, the public and the media have called for the removal of Amodu, who helped the country qualify for the 2002 FIFA World Cup.
However, the technical committee of the NFF has now thrown its weight behind Amodu and has asked him to continue in his job for the remaining two FIFA World Cup qualifiers in October and November.
"Taking panicky measures at this time may even worsen the situation. So sacking Amodu may not be the best solution to the problem at hand," said technical committee member Adeboye Onigbinde.
"If you now want to change the group of coaches with the technicians and personnel we have there now and if a new coach comes in, is he going to throw away all the players we used during the last match against Tunisia and bring down his own players? And how long does he have to do that? And what is going to happen?"
Former international skipper, Austin 'Jay Jay' Okocha has also been appointed as technical assistant to Amodu, along with businessman John Mastoroudes.
Amodu took over from German coach Berti Vogts in April 2008 after Nigeria crashed out in the quarter-finals of the CAF African Cup of Nations in Ghana.