Those paying close attention during President Bush’s Republican National Convention speech got a vague hint of his plans to expand federal funding to community health centers.

About a third of the way through, just before he transitioned from outlining his health care proposals to discussing new workplace regulations, Mr. Bush said the government would provide low-income residents better access to care and would ensure that “every poor county in America” had a health center.

The initiative is part of a five-year Bush administration plan that has, since 2002, provided funding for the opening and expansion of 946 “federally qualified health centers” nationwide. Last year, the federal government allocated $1.6 billion in grants to health centers and, this year, Mr. Bush is requesting an additional $219 million from Congress for what he says is an effort to “make sure people get preventative and primary care, not in the emergency rooms, but in these clinics for low-income Americans.”

While many in the health care community say the expansion is an important part of improving access to primary care doctors, there is also widespread concern the funding is not adequate, the application process is too arduous, and systemic problems are not being addressed.

“It’s a big step in the right direction and we are extremely grateful for the funding, but more needs to be done,” said the executive director of the Betances Health Center in Lower Manhattan, Wanda Evans. “We have 46,000 to 50,000 patient visits a year and health care costs are expensive.”

The Betances center was approved for $650,000 in annual grants to expand primary care services and add a dental clinic. But, Ms. Evans said, the center, which serves a large low-income and immigrant community, has seen an increase in uninsured patients and is contending with rising medical costs, in addition to providing the new services.

The National Association of Community Health Centers had requested an increase of $250 million for the upcoming fiscal year, but an official there said yesterday that organization was “thrilled” with the slightly lesser increase Mr. Bush proposed and by the “unprecedented” attention the White House was devoting to issue.

“He has made expanding these health centers a centerpiece in his health care platform,” said a spokeswoman, Amy Simmons, who touted the centers for their ability to stem chronic illness and to decreased emergency room visits.

If the Bush administration makes good on its promise, New York may be fertile ground for expansion. Of the state’s 62 counties, 32 do not have federally subsidized health centers and may be eligible for funding, said the executive director of the Community Health Association of New York State, Sheila Kee. Twelve were approved in 2003 under the program for grants of several hundred thousand dollars apiece.

Ms. Kee said she was pleased with Mr. Bush’s proposal, but said money is also needed for the existing facilities, whose financial solvency is susceptible to “one little sneeze.”

“This can help, it can make a dent, but it is by no means a solution,” she said.

Others said the same, noting that all medical institutions were feeling the effects of the 45 million uninsured, who often end up bypassing preventative care and going to the emergency rooms, where they end up costing the system more money.

Backers of the Bush plan say that is exactly why these expanded facilities are needed.

Where expanded and new facilities are likely to play a great role, experts said, is in bringing badly needed health care to rural areas that have an inadequate number of practicing family doctors.

“In many of these communities, families’ doctors have disappeared, so this is a really important contribution in replacing them,” said a professor of health policy and political analysis at the Harvard School of Public Health, Robert Blendon.

But, he added, the proposal has shortcomings.

“These facilities are great for primary care, but they are usually very light on specialty care and pharmaceutical needs,” Mr. Blendon said. “There is no continuity for someone with diabetes, or cancer, or some other advanced disease that needs a referral.”

Several sources also said they were concerned that only one in 10 health centers to date had been approved for the grants and that the funding was limited to operating expenses, not capital needs. The latter could result, they said, in more money for expansions and less for new facilities.

A spokesman for the Department of Health and Human Services, which is overseeing the grants, said 508 of the recently funded facilities are new. And, the measure is only one of the myriad plans that Mr. Bush is proposing, said the spokesman, Bill Pierce.