LISBON (Reuters) - Portugal's government is seeking support from the main opposition party for 4 billion euros of new spending cuts that may need changes to the constitution to push through, the prime minister said.

"We will review certain structures and functions of the state to achieve a spending reduction of 4 billion euros (by) 2014," Pedro Passos Coelho told reporters late on Monday.

With the country struggling to meet the fiscal goals set under its 78 billion euro EU/IMF bailout, the premier said he would invite the opposition Socialists to join discussions on the cuts on Tuesday.

A parliamentary debates on the 2013 budget bill, which would impose sweeping tax hikes and which the Socialists have said they will oppose, gets under way during the day.

The government had earlier said it would work on spending cuts in addition to those already budgeted for in 2013. Next year's budget deficit goal of 4.5 percent of gross domestic product equals a gap of around 7.5 billion euros.

The International Monetary Fund warned earlier this month of growing risks to the deficit reduction programme due to lower tax revenues, growing popular resistance to austerity and the likelihood that the country will remain in recession next year.

The government has a comfortable majority to pass bills in parliament, but a constitutional amendment would require support from two thirds of lawmakers - which would have to include the Socialists.

"We may have to revise some aspects of the constitution for this effect (spending cuts), but it is not a pre-condition," Passos Coelho said.

It was the country's previous Socialist administration that requested the international bailout in April 2011.

The austerity measures needed to hit the targets set under the rescue programme enjoyed cross-party support until last month, when the government's tax hike plans and a worsening economic outlook broke the political consensus.

The Socialists have said they support the bailout and its targets as a whole but reject Passos Coelho's "austerity at all costs" policy. The debt crisis and the austerity have fuelled the country's worst recession since the 1970s.

The opposition wants the belt-tightening to focus more on spending cuts than tax hikes, but without undermining Portugal's welfare state a condition that is likely to make any discussions on spending cuts problematic.

($1 = 0.7749 euros)

(Reporting By Filipe Alves and Andrei Khalip; Editing by John Stonestreet)