Source: Sharecast
The initial reading of the composite purchasing managers' index (PMI) was 50.2 for January, up from 49.6 in December, according to S&P Global and the Hamburg Commercial Bank (HCOB).
This was the first reading above the neutral 50-point level since August and ahead of market expectations of 49.7.
The services PMI slipped to 51.4 from 51.6, marking the second straight month of growth, while the manufacturing PMI increased to 46.1 from 45.1.
Nevertheless, Eurostat still highlighted that the overall growth in private sector output was "only marginal [...] amid ongoing demand weakness".
Encouragingly, there were signs of improvement in the eurozone's largest economy, Germany, with business activity stabilising after six months of declines, though activity in France remained in contraction.
Cyrus de la Rubia, chief economist at HCOB, said the "kick-off to the new year was mildly encouraging".
"In a surprising twist, employment in the service sector increased more robustly than in December, when it barely grew. It's also encouraging that services incoming new business, which had either shrunk or broadly stagnated over the last four months, returned to growth. However, the situation remains fragile as outstanding business shrank again, and the same goes for new export business, which includes tourism."