BRUSSELS, July 2 (Reuters) - The European People's Party, the biggest lawmaker group in the European Parliament, will seek to weaken the bloc's planned 2035 phase-out of CO2-emitting cars, a draft document showed.

The EPP won the biggest share of any lawmaker group in last month's European Parliament elections with 188 out of the total 720 lawmakers, cementing its influence in the EU assembly.

At a meeting in Portugal this week, lawmakers from the group are discussing policy priorities for the EU Parliament's next five-year term.

A draft of those priorities, seen by Reuters, included the aim of: "revising the rules for CO2 reduction for new cars and vans to allow for the use of alternative zero-emission fuels beyond 2035".

The EU passed a policy last year that will ban sales of new CO2-emitting cars in 2035, effectively ending sales of new combustion engine vehicles running on petrol and diesel.

The European Commission has pledged, however, to create a legal route for sales of new cars that only run on "e-fuels" - synthetic fuels that can be used in a combustion engine car instead of petrol - to continue after 2035, after Germany demanded this exemption.

That could allow carmakers to develop and keep selling a new breed of combustion engine cars that only run on certified CO2-neutral fuels, and are equipped with technology to prevent them from starting when filled with petrol or diesel.

The EPP did not specify in what ways it would want the car CO2 policy changed. The document added that the group wanted to "revise the ban on combustion engines and develop cutting-edge combustion engine technology".

The draft document, if taken forward by the EPP, will pressure European Commission Ursula von der Leyen - who belongs to the EPP group - over how she will manage Europe's green agenda, as she seeks approval from a majority of EU lawmakers for a second term in her role.

Von der Leyen needs the EPP group's backing to secure a majority - but she faces the challenge of also needing to win over groups including the socialists and democrats, which are opposed to weakening Europe's policies to fight climate change. (Reporting by Kate Abnett; Additional reporting by Victoria Waldersee; Editing by David Holmes)