It was a game of few chances with goalkeepers Antonio Tono and Andres Fernandez both proving equal to what was thrown at them.
Both teams now sit on 26 points, just five above the relegation zone ahead of the rest of the weekend's fixtures.
Oriol Riera had the first chance for the visitors after five minutes and should have done better with a close-range header, but Tono was on hand to parry.
Cristian Herrera then fired wide from just six yards as Elche got a foothold in the game and Fernandez was forced into a save as Ruben Perez tried his luck from distance.
Herrera sent a header wide shortly after, but it was Osasuna who had the best chance as Alejandro Arribas got his head on to a corner and Tono did brilliantly to tip over the bar.
Carlos Sanchez was next to fire a header over the bar just before the half hour as the opening period drew to a close.
Roberto Torres brought a save from Tono just after the break in an otherwise quiet opening to the second half with Niguez Aaron's speculative effort the only reply from Elche.
Torres was the man looking the most likely to break the deadlock and with 10 minutes to go he brought a smart save from Manu who had replaced Tono in the Elche goal.
Both sides continued to search for a winner in the closing stages but never really looked like finding one as the game wound down.