The NHS plans to spend £100m bringing in up to 3,000 GPs from abroad to help alleviate serious shortages that have left surgeries struggling to run properly.

Recruitment agencies will earn about £20,000 for each GP they succeed in placing in a family doctor practice in England as part of the NHS England initiative.

The scheme will have to persuade significant numbers of doctors working overseas to relocate to England if the government is to fulfil its pledge to boost the number of GPs by 5,000 by 2020.

The most recent NHS Digital figures show that the number of full-time equivalent GPs is falling, from 29,862 in September 2015 to 29,423 in June – a decline of 439.

NHS England initially said it wanted to recruit 500 extra GPs from abroad. But it has significantly increased that target to between 2,000 and 3,000 to help tackle what it calls “a gap between the number of doctors practices want and the numbers they are successfully recruiting and retaining”.

It said last week: “Many practices continue to face recruitment issues, and newly qualified GPs are often working as locums rather than joining a practice as a permanent GP [and] GP training places … are not yet filled at 100% levels.”

Opposition parties said the move symbolised the government’s failure to make good on its promise of 5,000 more GPs, first made by the health secretary, Jeremy Hunt, in the 2015 election campaign.

“This is evidence of the abysmal lack of progress made by the government in meeting its pledge to recruit an extra 5,000 GPs by 2020,” said Norman Lamb, the Liberal Democrats’ health spokesman. “Enormous sums that could have been spent on improving patient care will instead now be paid to recruitment agencies.”

Jonathan Ashworth, the shadow health secretary, said: “This is yet another example of the government’s financial mismanagement of our NHS and their lack of action when it comes to the GP workforce. Under the Tories, general practice is being stretched to breaking point, and patients are being let down as a result.”

A notice placed by NHS England advertising the £100m contract says it wants to finalise a “framework agreement of international recruitment service providers” with a maximum of eight recruitment firms. They will then recruit the GPs before April 2020 and also help them prepare for working in England and to relocate with their families.

NHS England hopes that many of the extra GPs will come from Europe. Despite the risk that Brexit will deter health professionals from choosing to work in Britain, it is “rapidly expanding the current international recruitment programme of doctors from the European Economic Area, whose GP training is recognised in the UK under European law and [who] already get automatic recognition to join the General Medical Council’s GP register”.

The NHS’s massive overseas recruitment of GPs may become a test of the arrangements that are eventually put in place to control foreign nationals’ right to work in the UK after Brexit.

“We are calling for GPs to be added to the migration advisory committee’s shortage occupation list, to make it easier for family doctors from overseas who want to live here and work in UK general practice to do so,” said Dr Steve Mowle, the honorary treasurer of the Royal College of General Practitioners.

Both the RCGP and the British Medical Association welcomed the move. The college called it a bold step.

“Overseas doctors have for many years provided outstanding levels of care to patients across the NHS and with the current problems facing the GP workforce could provide valuable help in maintaining struggling services,” said Dr Krishna Kasaraneni, the BMA’s GP workforce lead.

But he added: “The government needs a long-term plan that addresses the fundamental pressures on general practice from rising patient demand, stagnating budgets and widespread GP shortages. Even taking into account recent announcements, the government is still going to be well short of its target of recruiting 5,000 new GPs by 2020.”

Mowle said the extra GPs were “desperately needed” and said ministers and NHS bosses needed to deliver all their pledges to general practice – such as 5,000 more practice staff including nurses and pharmacists – to tackle its “resource and workforce crisis”.