Tim Ryley, chief executive of Leeds Clinical Commissioning Group (CCG), said the problem was “if anything getting worse” across the country.
Mr Ryley, whose organisation oversees local NHS services, said that although Leeds was coping better than other places, it was still overwhelmed.
Speaking to city councillors at a scrutiny meeting on Tuesday, he said: “There’s a known gap of 5,000 GPs (across England).
“If anything it’s getting worse. It’s not going in the right direction.
“Leeds is relatively well provided for, partly because we have a medical school and people generally end up working in practices near where they trained, quite often.
“But that gap in the workforce remains a significant problem.”
Mr Ryley added that the staff shortage was “not conducive to delivering the kind of service and opportunities we’d want to see.”
He added, however, that GPs were currently working harder than ever to see patients.
He revealed that around one-in-three people in Leeds have some form of consultation with their doctor every month.
Mr Ryley said: “When we hear stories, and I hear them regularly as an NHS manager, from people saying, “I can’t get hold of my GP,” I think the assumption sometimes is that GPs aren’t doing anything.
“GPs are doing probably the most to increase their productivity than any other part of the economy.
“But nevertheless there are still not enough GPs to meet the level of demand.
“It takes around 10 years to train a GP, so this isn’t a problem that’s being resolved quickly.”