Italy began a week of strikes by the three biggest labour unions against Prime Minister Mario Monti's 33-billion-euro austerity package, which the government may soften slightly to meet some of their demands.

Port, highway, and haulage personnel stopped work for three hours and metal workers -- including those at carmaker Fiat -- put down their tools for eight hours. Printing press operators stopped for a full shift and most newspapers won't publish on Tuesday.

Public transport strikes will be held on Dec 15-16. Bank employees will halt work for the afternoon of Dec 16, and the public administration will close down for a whole day on Dec 19.

For the first time in six years of division, the three main union leaders shared a stage together when they spoke to striking workers in front of parliament.

We're not giving up on the idea that the austerity package must be changed, Susanna Camusso, chief of the largest labour group Cgil, told the crowd.

It hurts workers, pensions and the country as a whole, she said.

Monti failed to thwart the strikes during a last-ditch meeting on Sunday night with union leaders.

Monti underscored the extreme urgency of his government to act to restore investor confidence amid a euro zone debt crisis, and said he was open to amendments as long as they can be fully funded, according to a statement.

Union opposition will not affect parliamentary support for the package, Pier Luigi Bersani, secretary of the centre-left Democratic Party (PD), said on Monday. The PD counts many union members among its supporters.

Bersani told Corriere della Sera daily that he shared union concerns about the effects of the tax increases and pension cuts on low incomes, but his party's backing was still assured.

We will be responsible. Our support isn't in discussion, he said. This budget correction is a message to Europe.

UNFAIR

Unions accept the need for more austerity but say Monti's plan is unfair. Rather than raising money by taxing pensioners and low earners, the government should be boosting levies on the wealthy, they say.

We are here to show our opposition towards the new economic measures that the new government is putting together, said Sergio Bussone, one of the striking union members in the capital. These measures punish public sector workers, and will be harmful and negative for all the pensioners.

As yields on Italian 10-year bonds exceeded the critical 7 percent level, Monti on Dec 4 introduced a raft of measures including pension reform and hikes in property tax, sales tax and petrol tax.

Borrowing costs fell sharply on optimism ahead of a European Union summit last week but have since crept back up, and rose above 6.8 percent on Monday after the summit failed to provide an immediate solution to the euro zone debt crisis.

ECB intervention helped yields back to 6.6 percent.

To meet demands from both unions and parties, the government is seeking other revenue sources or spending cuts to alleviate cuts to low pensions and to give property-tax exemptions to low-income families.

The total cost of both moves would be 5 billion euros, parliamentary sources said. On Monday, lawmakers pushed back the deadline to amend the package by 24 hours to late Tuesday.

(Reporting By Giuseppe Fonte, Francesca Piscioneri, Cristiano Corvino, and Steve Scherer; editing by Philippa Fletcher)