* Climate policies passing through EU lawmaking process

* EU parliament committee backs tougher CO2 market rules

* New CO2 market scaled back to exempt consumers until 2029

BRUSSELS, May 17 (Reuters) - Lawmakers on the European Parliament's environment committee voted on Tuesday for a more ambitious overhaul of the EU carbon market than previously proposed, as they prepare to negotiate reforms to the bloc's core emissions-cutting policy.

Europe's carbon market forces power plants and factories to buy CO2 permits when they pollute. It has slashed emissions in those sectors by 43% since 2005, but is facing a revamp to hit more ambitious EU climate change targets.

A narrow majority in the committee backed proposals to cut the supply of permits in the carbon market faster, to slash emissions covered by the scheme by 67% by 2030 from 2005 levels. The European Commission, which drafts EU laws, had proposed a 61% cut.

Parliamentary groups the Greens, Socialists and Democrats, Renew and the Left backed the plan to cut the supply of permits added to the market by 4.2%, and boost the rate by 0.1 percentage point per year to ensure emissions fall faster. A one-off supply cut to remove spare permits would also apply.

The more ambitious changes may struggle to win majority support when the full EU assembly votes on them in June, however. Unicredit analysts on Tuesday saw a "modest" chance of the whole parliament approving them, but said they expected EU countries to resist.

A majority in the committee backed changes making it easier to intervene in the carbon market if prices spike. If the CO2 price for six months is more than twice as high as the average over the two previous years, policymakers can consider adding more permits to the system.

The committee also voted to end free CO2 permits for industry by 2030, replacing them with a carbon border levy on imports of polluting goods. The Commission had proposed a more gradual free permit phaseout, by 2036.

The lawmakers voted to scale back plans to launch a second emissions trading system (ETS) to impose CO2 costs on suppliers of fuels used in buildings and transport, a proposal that has faced opposition from some lawmakers and countries.

The committee agreed to apply the scheme to commercial entities from 2025, and only extend it to private consumers in 2029 if certain conditions are met. It will be accompanied by a fund to shield vulnerable households from any resulting costs.

"Even though I would have wished for a broader approach, I am happy that ETS II is alive and kicking," said EPP lawmaker Peter Liese, parliament's lead negotiator on carbon market reforms.

The committee will confirm its position with another vote later on Tuesday. EU countries will agree their position on the reforms next month, before countries and lawmakers negotiate the final rules. (Reporting by Kate Abnett; Editing by John Chalmers and Jan Harvey)