Ministers from EU countries plan to agree on their position next week, before negotiating the final law with the EU parliament -- which supported the 2035 ban in a vote this month.
In a paper circulated among EU states, the five countries called instead for a 90 percent cut in car CO2 by 2035 and reaching the 100 percent target by 2040.
They said light commercial vehicles should meet an 80 percent CO2 cut by 2035 and 100 percent by 2040, rather than the 100 percent reduction by 2035 proposed by the Commission.
"Adequate and tailored transition periods need to be established," the paper said, citing the need to expand charging infrastructure.
A Bulgarian official, who did not wish to be named, said climate policies needed to consider economic and social factors such as the "the significant differences" in purchasing power between EU countries.
Brussels says the 2035 date is crucial because the average lifespan of new cars is 15 years -- so a later ban would stop the EU from reaching net zero emissions by 2050, the global milestone scientists say would avert disastrous climate change.
Some EU governments have rallied behind the 2035 target, but Germany's finance minister said this week the EU's biggest car market would not support it.
Ford and Volvo Cars have publicly supported the plan, and Volkswagen aims to stop selling combustion engine cars in Europe by 2035. But industry groups including the European Automobile Manufacturers' Association have opposed the 2035 target, citing concerns including the uncertain rollout of chargers.
The EU is negotiating another law requiring countries to install millions of vehicle chargers this decade.