(Abridged) We performed a deep infrared imaging survey of 63 embedded young stellar objects (YSOs) located in the Taurus and Ophiuchus clouds to search for companions. The sample includes Class I and flat infrared spectrum protostellar objects. We find 17 companions physically bound to 15 YSOs with angular separations in the range 0.8-10 (110-1400 AU) and derive a companion star fraction of 23+/-9 % and 29+/-7 % for embedded YSOs in Taurus and Ophiuchus, respectively. In spite of different properties of the clouds and especially of the prestellar cores, the fraction of wide companions, 27+/-6 % for the combined sample, is identical in the two star-forming regions. This suggests that the frequency and properties of wide multiple protostellar systems are not very sensitive to specific initial conditions. Comparing the companion star fraction of the youngest YSOs still surrounded by extended envelopes to that of more evolved YSOs, we find evidence for a possible evolution of the fraction of wide multiple systems, which seems to decrease by a factor of about 2 on a timescale of about 10^5 yr. Somewhat contrary to model predictions, we do not find evidence for a sub-clustering of embedded sources at this stage on a scale of a few 100 AU that could be related to the formation of small-N protostellar clusters. Possible interpretations for this discrepancy are discussed.
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