output of all euro zone states, but rising exports are also helping to revive the manufacturing sectors of other countries, most notably Spain and Italy," Williamson said.
An improvement in export orders, which include purchases from within the bloc, came despite the euro hitting an 11-month high last month on signs of an economic upturn in Germany and hopes the euro area banking system may be on the mend.
Last year, European Central Bank President Mario Draghi promised to do "whatever it takes" to save the euro, triggering a rally in European stock markets and easing the sovereign debt crisis as borrowing costs plunged.
Backlogs of work were run down at their weakest rate since July 2011, with the sub-index rising to 47.1 from December's 45.1, in a further signal that order books were filling up.
But factories were forced to cut their prices for the seventh time in eight months, despite rising input costs, to drum up business and instead reduced headcount to increase profitability.
Official data due later on Friday is expected to show unemployment rose to a euro-era high of 11.9 percent in December.
Markit's PMI for services firms, which account for the vast bulk of the euro zone's private economy, is due on Tuesday and is expected to show the rate of decline eased.
(Editing by Hugh Lawson)