The EU is set to emit 2bn tonnes more CO2 than it promised at the Paris climate talks, threatening an agreement to cap global warming at 2C, a note from the European commission has revealed.

Carbon prices will rise too slowly to cut industrial emissions as much as needed, says a confidential note prepared for MEPs on the environment committee, which the Guardian has seen.

Lawmakers say that the shortfall could spur criticism from other countries that signed up to the Paris agreement, which aims for net zero emissions later this century.

But a correction in the pace at which carbon allowances are removed from the market - to raise their prices - could spark anger from coal-dependent EU countries such as Poland, which believes its industry would be unfairly hit.

The EU was “caught between a rock and a hard place” said the Green MEP Bas Eickhout, who sits on the environment committee.

“The current proposals are not consistent with what was agreed in Paris and they are not even in line with what’s necessary to stay below 2C,” he told the Guardian. “What kind of signal is that sending our partners? These Emissions Trading System (ETS) numbers need to be changed now to make them consistent with the Paris agreement.”

Seb Dance, the Labour party’s environment spokesman, who also sits on the committee, said: “If we do not raise the level of ambition and move towards a greater linear reduction factor for the ETS, the UK and other EU countries will not meet the groundbreaking climate change targets agreed in Paris.”

The reason for the CO2 overshoot lies in an EU decision to make its ETS the only lever to ratchet emissions down, when renewable energy and efficiency targets end in 2020.

The ETS’s “cap and trade” scheme creates a limited emissions market, within which 11,000 power stations and industrial plants can buy or sell allowances.

It is lauded by supporters for a market-based approach that rewards greener firms with tradable credits, while encouraging dirtier firms to clean up their act, or offset their emissions by paying for accredited emissions cuts elsewhere.

Critics have raised questions about the veracity of some of these schemes, the over-allocation of free allowances to heavy polluters, and the extent to which prices – currently hovering at around €5 a tonne – can help fuel switching.

The system does have a mechanism to gradually reduce the number of carbon credits available - and so raise prices - but the note says that this will not be enough to cut emissions to at least 80% of 1990 levels by 2050, as the EU has promised.

Europe would emit more than 2bn tonnes of CO2 because of the carbon accounting problem, according to an analysis for the Guardian by the campaigning group Sandbag.

By 2050, the cost of the carbon credits needed to account for this extra CO2 would be €146bn the group estimated, based on price ranges used in a European commission impact assessment.

Damien Morris, an analyst for Sandbag, said that Europe needed to remove a higher number of allowances from the ETS, more quickly: “This is what is needed just to align the carbon market with the current EU goal in its low-carbon roadmap. After Paris, though, Europe should be looking to go significantly further than this.”

The Paris agreement proposed an aspirational cap on global warming of 1.5C. A draft commission summit analysis said that a communique would be produced by 2019 to spark a debate on the “profound lifestyle changes” needed for this to happen.

