About 90 percent of District of Columbia's 75 independent pharmacists yesterday struck the city's Medicaid program, refusing to fill prescriptions for the poor until the city agrees to give the businessmen a 10 percent rate increase.

The strike could have a direct effect on the lives of the 118,000 poor persons whose health care is paid for by the joint local-federal health insurance plan.

The druggists are now paid $2.59 - plus the cost of the drugs - for each Medicaid prescription they fill. That rate was set after a similar two-week strike last year.

"Some people will have to pay for the medicine out of their own pocket and they won't be able to get food," said Marty Hauer, a pharmacist who is acting as one of the spokesmen for the strikers. "Some people are not going to get their medicine and they're going to end up in the hospital. But the city cannot expect the (pharmacists) to pick up the cost" of the Medicaid program.

According to City Administrator Elijah Rodgers, who said the city does not have the money to pay for increased drug costs, the chain drug stores in the city, such as Peoples, Giant and Dart, can pick up the Medicaid business. Medicaid patients can also go to city department of Human Resources pharmacies, said Rogers.

In fiscal 1977, the city's pharmacists - including the chains - received about $5.1 million, or 6.7 percent of the money paid by Medicaid to the private sector, which includes payments to doctors and hospitals.

According to Dale Morton, a leader of the current strike as well as last year's "were forced to do this (each year because) DHR will not come across with a cost of living increase yearly.

"We asked for a cost of living increase, we asked for a mechanism for a review (of the cost of filling a prescription), and we asked for a fee increase. And the answer was 'no'," said Morton.

According to Morton, at a meeting a month and a half, ago, Rogers, when told the pharmacists were losing money by participating in the program, asked, 'Why are you in the program? . . . If you're not making any money, why are you in the program?

Rogers yesterday denied making the statement, which is being widely quoted by striking pharmacists. "It's a very difficult time for everybody in public service," Rogers said, "including the government. If they get a Medicaid increase, then other (providers) will come in and ask for a rate increase."

That is precisely what happened last year, when the pharmacists were granted an increase from $1.80 to $2.59, a sum slightly lower than that paid in Virginia and slightly higher than the fee paid in Maryland.

At that time the city also raised the payments received by other Medicaid providers, including physicians, who had not received an increase since the Medicaid program began here in 1968.

Many of the more than 1,400 physicians who serve Medicaid patients complain that some of the payments they receive cover as little as one quarter of the amount they charge private patients, forcing them to serve Medicaid patients at a loss.

Morton, who said that Medicaid accounts for about 90 percent of the prescription business at one of his two pharmacies, says that the $2.59 does not cover the overhead involved in preparing prescriptions.

According to Rogers, the city is seeking money in its 1980 budget to give the pharmacists a rate increase. In the meantime, he said, his staff is determining the actual cost of filling prescriptions.

"I feel very badly about this," said Hauer. "Pharmacists traditionally have looked after the welfare of their patients. I'll sell a patient a day or two's supply if he can only afford that, rather than a month's supply. If it's nitroglycerin (for heart conditions), or if it's blood pressure medicine, I'll give them the medicine."