RCGP chairwoman Professor Clare Gerada warned the plans would put pressure on GPs but generate minimal cost savings.
GPC chairman Dr Laurence Buckman said the BMA would 'strongly oppose' any plans that would make GPs act as 'border force agents'.
The proposals are part of a cross-government consultation that aims to 'make it more difficult for illegal migrants to live in the UK unlawfully, and to ensure legal migrants make a fair contribution to our key public services'.
Health secretary Jeremy Hunt said: 'We need to ensure that those residing in or visiting the UK are contributing to the system, but we want to implement a system that limits red tape for NHS professionals.'
Proposals include a £200 annual NHS levy for people applying for UK visas who do not have private health insurance.
The government could impose further charges for GP visits on patients visiting the UK for less than six months, and has not ruled out asking practices to collect the fees.
Mr Hunt added: 'We are clear that the NHS is a national health service, not an international health service, and I am determined to cut out abuse in the system.'
Professor Gerada told the BBC the plans would increase the burden on doctors. 'My first duty is to my patient. I don't ask where they're from or whether they've got a credit card.'
The amount spent each year treating people who are ineligible amounted to just two hours of NHS spending, she added.
The NHS estimated in 2011/12 that it spent £33m treating foreign nationals, £21m of which was recovered, with £12m written off. The annual NHS budget is about £110bn.
GPC chairman Dr Laurence Buckman said the BMA would 'strongly oppose' requiring GPs to act as border agents or enforce immigration checks.
'Doctors should spend their time treating patients, not acting as the arbitrators of whether patients are eligible to receive NHS care,' he said.
'If abuse of the system is taking place, measures should be in place to stop this, but we need to hear more from the government on how this can be realistically achieved.'
Dr Buckman warned: 'The botched launch of NHS 111 demonstrates what can happen if a system is rushed through because of politically driven deadlines.'
But Bedfordshire and Hertford-shire LMCs chief executive Dr Peter Graves said GPs who had raised concerns about the problems would be 'delighted' that the government was listening.
'Those are the people who really need to understand that we just can't afford to give them free treatment when they come here specifically for that purpose,' he said.