The American Civil Liberties Union, charging the government of El Salvador with continuing repression, including responsibility for an estimated 12,501 murders during 1981, yesterday urged President Reagan not to certify to Congress that the Salvadoran regime is improving its human rights record.

The ACLU and another private organization, the Americas Watch Committee, made public a 273-page report detailing charges of systematic murder, torture, arbitrary arrests and denial of rights by the U.S.-supported civilian-military government headed by President Jose Napoleon Duarte.

Under the foreign aid legislation passed last month, Reagan must certify to Congress by the end of this week that the Duarte government, in exchange for U.S. military assistance to fight leftist guerrillas, is making "a concerted and significant effort" to comply with international human rights standards and is "achieving substantial control over all elements of its armed forces."

The ACLU, which normally is concerned with safeguarding liberties in this country, has had a general policy since 1973 of opposing U.S. aid to countries engaged in rights violations. However, ACLU officials said yesterday that the report on El Salvador marked the first time the organization has singled out a specific government as being in violation of that policy.

State Department spokesman Alan Romberg declined to comment on the report and said the administration's position will be spelled out in detail when the president sends the required notification to Congress later this week.

It is known that the administration will dispute the continuing criticism directed against the Duarte government by human rights organizations and congressional liberals. The administration will contend instead that, under Duarte's leadership, the Salvadoran government has been making significant strides in correcting past abuses and moving the country toward democracy.

Many of the rights violations described in the report involve incidents that occurred prior to this past year. However, the report notes that Salvadoran authorities, citing the necessities imposed by civil war, have continued the suspension of constitutional rights guarantees.