* Lower house of parliament backs 2014 supplementary budget
* Rebel Socialists warn over social security budget vote
* Bill combines spending cuts, tax relief for households
* France targets 2014 public deficit at 3.8 pct of GDP (Adds details on bill, further vote next week)
PARIS, July 1 France's lower house of parliament backed a supplementary budget for 2014 by a large majority on Tuesday, a relief for President Francois Hollande as his Socialist party managed, for now, to contain opposition within its own ranks.
Together with the social security budget on which lawmakers will vote next week, the updated budget plans an extra 4 billion euros in public spending cuts and tax relief for nearly 4 million households as Paris tries to meet deficit targets while assuaging concerns of disgruntled voters.
The two bills had become the focus of discontent among Socialist lawmakers, with some saying Hollande was doing too much to cut tax on business and not enough to help low and middle-income households.
About a tenth of Socialist lawmakers had tried to push amendments through. But they eventually agreed to back a text that went some way to meeting their concerns, bringing 3.7 million households a total of 1.1 billion euros in tax relief.
The budget bill was adopted by 307 votes to 232.
However, the government still has to face opposition among Socialist lawmakers on the social security leg of the budget, which will be voted on next Tuesday.
One of the spokesmen of the rebel group, National Assembly deputy Christian Paul, said they could not pass a bill he said "finances support to business by freezing welfare subsidies."
The budget bill aims to keep France on track with its plan to bring its public deficit down to 3.8 percent of GDP this year and 3 percent - the EU target - next year. The European Commission warned last month it considered France's forecasts too optimistic and that it needed to do more to meet EU deadlines in 2015.
The bill also includes a new system of road tolls to replace a plan for nationwide charges on heavy vehicles. That proposal was abandoned earlier this year amid widespread protests.
The budget is based on a government forecast of 1 percent growth, which most - including official statistics office INSEE - deem too optimistic.
In a fresh warning on growth, a survey by data compiler Markit showed on Tuesday that French manufacturing activity shrank at the fastest rate in six months in June as firms cut production for the first time in five months and new orders dropped at the quickest rate this year.
Hollande, the most unpopular president in French polling history, is under pressure from some of his fellow Socialists to loosen fiscal policy. But he also faces a growing campaign by employers' groups for more guarantees on tax relief and changes to some labour reforms.
Employers have threatened to boycott an annual conference with labour unions on July 7-8 aimed at discussing reforms.
The supplementary budget bill will now go to the Senate, the upper house of parliament, before a final National Assembly vote on July 15. (Reporting by Emile Picy; Writing by Ingrid Melander; Editing by Mark John, Alexandria Sage and Mark Trevelyan)