GPonline has obtained a letter sent last month by the GPC to NHS England, demanding national suspension of the QOF.
LMC leaders in Leeds secured a deal this week with the city's three CCGs to suspend the framework for the rest of 2016/17, with practices protected from financial losses.
Other LMCs have opened talks with CCGs in their area to push for similar deals.
The GPC letter, dated 25 January, points to deals to suspend the QOF in Wales and Northern Ireland, and the scrapping of QOF altogether in Scotland. It warns that there is 'absolutely no doubt' that practices in England are facing extreme workload pressure.
It says: 'At such a time as this it is imperative that NHS England does all it can to relieve this pressure so that practices can prioritise the care of urgent cases and provide support to the most vulnerable.
'Whilst practices will already have done most of the work to achieve QOF indicators this year, removing the requirement to achieve these targets will reduce unnecessary bureaucratic burdens and send an important signal of support to GPs in England at this challenging time.'
GPC chair Dr Chaand Nagpaul told GPonline that the committee was frustrated that NHS England had not agreed to a national suspension of QOF.
He said that with national frameworks such as the QOF, he believed that changes should be applied nationally. 'If NHS England has a system that allows local deals to be done, it does not make sense that this could not be a national deal to ease pressures on general practice,' Dr Nagpaul said.
The GPC chair accepted that in Leeds there had been specific additional circumstances - problems with a pathology service that left practices facing significant additional workload - that were a factor in the decision to suspend QOF. But he warned that pressure everywhere on practices was high, and said he was disappointed at NHS England's failure to accept the call for a national QOF suspension.
The dispute over QOF suspension comes as the GPC seeks to complete negotiations on the 2017/18 GP contract. The process is understood to be close to completion. Dr Nagpaul told GPonline: 'The GPC would have preferred negotiations to have finished earlier to allow practices to prepare. We are making every effort to conclude this as soon as possible.'