Fourteen people have died of heroin overdoses in Washington in the first three weeks of this month, more than in any month since medical examiners began keeping statistics in 1971, police reported yesterday.

The figure was released yesterday by District police, who expressed a growing concern about the recent influx of unusually pure quantities of the drug. The deaths bring the number of heroin abuse fatalities so far in 1981 to 37, compared with 17 at this time last year.

"The quality and quantity of the heroin available in Washington today is on a par with what it was 10 or 12 years ago," said D.C. narcotics detective William Larman last night.

The increase was not unexpected, narcotics investigators said. It coincides, they said, with the increased availability in the last two to three years of Iranian and other Middle Eastern or "Golden Crescent" heroin. Easier access to supplies, they pointed out, leads eventually to more heroin on the streets, and expanded competition among dealers. This competition usually leads to the sale of purer heroin, a move designed to keep customers happy but one that frequently leads to injection of lethal doses that exceed the tolerance of the user.

"It's a very sobering thing when you see three people who died of overdoses in one day, which happened last Friday," said the city's chief medical examiner Dr. James L. Luke. "Then it happened again yesterday."

A number of the most recent deaths, Larman said, were traced to sales made near 11th and O streets NW -- one of a dozen active sidewalk drug sale areas in the city. Larman said dealers recently have been attaching "brand names" to the heroin packets they sell, and said investigations have found that the most lethal variety currently for sale carries the name, "Murder I."

Last year, police recorded 62 deaths caused by drug overdoses, compared to 41 in 1979 and only seven in 1978. Luke said that the previous high toll for any month was 13 recorded in January 1972.

"Unless there is some drastic drop-off," said Larman, "this is going to be an all-time high for overdose fatalities in the history of the city."

Luke said the average age of this year's victim was 29.7, compared to 32 last year. Twenty-five of the victims were found to have alcohol in their systems -- 19 of them with more than 0.1 percent in their bloodstream, the legal equivalent of intoxication.

The oldest overdose victim this year was 55, Luke said. The youngest was 20.

"The 14 deaths are the most recorded in one month since the medical examiner system was created in 1971," said Luke. "And there's still 10 days left in this month."

Larman said tests made on a powder sample discovered at the side of one recent overdose victim showed the heroin to be roughly 7 percent pure compared to an average purity level of between 2 1/2 to 3 percent, he said.

Police officials theorized that Washington is becoming more of a "wholesale" drugs center than was true in the past.

"Drug dealers are not just traveling to various cities and bringing back street-level percentages to Washington any more," Larman said. "They're bringing back large amounts and cutting it and distributing it here, just like you find in other, larger drug centers, cities where drugs have traditionally been coming in large amounts."

Like New York? he was asked.

"Like New York," he said.