The college said the 'outstanding' response to the petition, which calls for general practice to receive a greater share of the NHS budget, showed patients were 'really getting behind the campaign'.
General practice delivers 90% of patient contacts for only 8.4% of NHS funding, the lowest share on record.
The petition, launched at the end of July under the college's Put patients first: Back general practice campaign, calls for an 11% share of funding by 2017. The college hopes to deliver 1m patient signatures to Prime Minister David Cameron and first ministers in the devolved nations next month.
Practices have been asked to collect signatures from their patients using a petition booklet available from the college. The deadline for returning the booklets has been extended to mid-September, when they will be counted ahead of the party political conferences.
The college will send out letters next week urging GP practices across the UK to return their completed petitions.
Dr Helen Stokes-Lampard, RCGP honorary treasurer, said: 'We have had an outstanding response to our petition with thousands of signatures being returned to our offices every day. It shows that patients are really getting behind the campaign.
'I would like to thank every patient who has signed the petition and all the GPs, practice managers, and other members of practice staff and patient groups who have facilitated the roll-out of the petition whilst already managing intense workloads.'
Patricia Wilkie, chair and president of the National Association for Patient Participation, said: 'The excellent response to the petition so far shows how concerned so many patients are about both the pressures facing general practice, and the need to put more NHS funding into GP services, where the great majority of patient contacts with the NHS take place.
'More resources would ensure that patients receive the service they need and that GPs want to give.'
Ceara Glackin, practice manager at the Holywell Surgery in Watford, said: 'We feel this petition has been a massive success locally, and the support we received for it was tremendous.'