By Balazs Koranyi and Francesco Canepa

FRANKFURT (Reuters) -Euro zone inflation has entered a new phase which could linger for some time, European Central Bank President Christine Lagarde said on Tuesday, outlining a lengthy fight against price growth that must dampen demand and force firms to curb prices.

The ECB has raised rates at each meeting over the past year, taking its deposit rate to 3.5%, and promised more tightening as soon as July as it attempts to curb inflation still running at three times its 2% target.

The issue, Lagarde argued, is that what was initially a transitory, energy-shock driven inflation has now seeped into the broader economy and could linger.

"It is unlikely that in the near future the central bank will be able to state with full confidence that the peak rates have been reached," Lagarde told the ECB Forum on Central Banking in Sintra, Portugal.

Workers, who lost their real earnings to inflation are now trying to recoup their losses, keeping inflation under pressure, a process that is amplified by lower than expected productivity growth, she said.

A recession would be expected to shake out the labour market, making the ECB's job easier but firms, remembering the difficulty of hiring back workers after the pandemic, are now hoarding labour, putting upward pressure on wages.

"This is weighing on productivity growth and... the motivation for firms to hoard labour may not disappear quickly," Lagarde said.

Another issue is that much of the recent employment growth is in sectors with low productivity growth, so high nominal income growth comes with weak efficiency gains.

"All this means that we will face several years of rising nominal wages, with unit labour cost pressures exacerbated by subdued productivity growth," she said.

Firms can hoard labour because they have raised their profit margins in recent years, and the ECB must keep pressure on them to adjust their pricing behaviour, she argued.

"We need to ensure that firms absorb rising labour costs in margins," Lagarde said. "This hinges on our policy dampening demand for some time so that firms cannot continue to display the pricing behaviour we have recently seen."

All this suggests that ECB policy must commit to holding rates at their peak level for an extended period.

"This will ensure that hiking rates does not elicit expectations of a too-rapid policy reversal and will allow the full impact of our past actions to materialise," Lagarde said.

Markets see the ECB's deposit rate peaking at 4%, suggesting that after July's 25 basis point increase, another move is likely, either in September or October.

(Reporting by Francesco Canepa and Balazs Koranyi; Editing by William Maclean and Christina Fincher)