Context : The nature of the early generation of massive stars may be inferred by investigating the origin of the extremely metal-poor ( EMP ) stars , likely formed from the ejecta of one or a few previous massive stars .

Aims : We investigate the rotational properties of early massive stars by comparing the abundance patterns of EMP stars with massive stellar models including rotation .

Methods : Low metallicity 20 M _ { \odot } stellar models with eight initial rotation rates between 0 and 70 ~ { } \% of the critical velocity are computed .
Explosions with strong fallback are assumed .
The ejected material is considered to fit individually the abundance patterns of 272 EMP stars with -4 < [ Fe/H ] < -3 .

Results : With increasing initial rotation , the [ C/H ] , [ N/H ] , [ O/H ] , [ Na/H ] , [ Mg/H ] and [ Al/H ] ratios in the massive star ejecta are gradually increased ( up to \sim 4 dex ) .
The ^ { 12 } C/ ^ { 13 } C ratio is decreased with initial rotation .
Among the 272 EMP stars considered , \sim 40 - 50 % are consistent with our models .
About 60 - 70 ~ { } \% of the CEMP star sample can be reproduced against \sim 20 - 30 ~ { } \% for the C-normal EMP star sample .
The abundance patterns of CEMP stars are preferentially reproduced with a material coming from mid to fast rotating massive stars .
The overall velocity distribution derived from the best massive star models increases from no rotation to fast rotation .
The maximum is reached for massive stars having initial equatorial velocities of \sim 550 - 640 km s ^ { -1 } .

Conclusions : Although subject to significant uncertainties , these results suggest that the rotational mixing operating in between the H-burning shell and the He-burning core of early massive stars played an important role in the early chemical enrichment of the Universe .
The comparison of the velocity distribution derived from the best massive star models with velocity distributions of nearby OB stars suggests that a greater amount of massive fast rotators was present in the early Universe .
This may have important consequences for reionization , first supernovae or integrated light from high redshift galaxies .