President Carter, overriding State Department objections, has sent a personal letter congratulating Nicaraguan President Anastasio Somoza for promises to improve the human-rights situation in his country.

Reliable sources said yesterday the letter has caused deep concern within the State Department because it was sent at a time when despite Somoza's promises, the department has been receiving reports of increased rights violations by the Nicaraguan National Guard.

The reports, which involve charges of renewed crackdowns against anti-Somoza forces in rural areas of the tiny Central American country, are expected to trigger new protests from liberal democratic governments in Latin America and human-rights activists in the United States.

For that reason, according to State Department sources who declined to allow use of their names, many department officials regard the timing of Carter's letter as a case of sending Somoza the wrong signal at the wrong time. State Department officials are concerned that revelation of the letter, which was supposed to be secret, will raise questions about the creditbility and sincerity of the administration's human-rights policy.

As a result, the sources said, the department ordered the U.S. embassy in Managua to delay delivering the letter to Somoza for several days while it tried to press these arguments at the White House. The White House refused to reconsider, and the letter was transmitted to Somoza in mid-July.

The incident could have repercussions in congress this week when the House votes on the administration's fiscal 1979 foreign aid package, which totals about $8 billion.

The request includes a $150,000 military training grant for the Nicaraguan National Guard, and there is a possibility that some liberal House members will seek to delete those funds on grounds that Nicaragua is guilty of extensive rights violations.

That, in turn, could endanger the already tenuous position of the entire aid package, because congressional supporters of Somoza have threatened to retaliate by introducing amendments to cut funds for other countries with poor rights records.

Administration sources who defended the letter called it an attempt to encourage Somoza to take positive steps toward relaxing his dictatorial rule, and thus not inconsistent with administration policy. These sources, while conceding that the letter had elicited objections from the State Department never actually recommended against sending it.

These differences within the administration are important because Nicaragua, which has been run by the Somoza family as a personal fiefdom for almost four decades, has assumed great symbolic status in the controversy over human-rights policy.

Since the beginning of this year, the country has been gripped with tension that has exploded into frequent violence. Rights activists within and without the United States have called repeatedly for the Carter administration to take a tough line with Somoza, while his friends have charged Washington with selectively picking on Nicaragua while ignoring rights violations in more strategically important countries.

In the face of these conflicting pressures, the administration frequently has seemed to veer back and forth, drawing charges from both sides that its policy toward Somoza is confusing, inconsistent and ineffective.

The Carter letter is likely to add to these charges. As pieced together from various sources, it appears to have come about in this way:

In mid-June, Somoza announced at a press conference that he planned to take several rights-improvements steps, including amnesty for some prisoners, allowing some exiles to return and inviting a visit by the Organization of American States Human Rights Commission.

That gave rise to a plan, apparently originating with the staff of the National Security Council, to give Somoza an encouraging pat on the back in the form of a letter from Carter. The letter was to be regarded as a personal communication to be treated by Somoza as confidential and not leaked to the press or used for political purposes.

A draft of the letter prepared by the NSC was forwarded to State for comment. David Newsom, undersecretary for political affairs, replied that State had several reservations and objections.

A second draft done at the White House pronounced an improvement by State, but the department made clear it still had reservations about the idea. In the meantime, the letter had been sent to Mauricio Solaun, U.S. ambassador in Managua, with instructions from State to delay giving it to Somoza until the White House had a chance to reconsider the matter.

Solaun help up the letter for more than a week. In the end, though, State was unable to get White House authorization to pull the letter back, and Solaun was instructed to transmit it to Somoza in a private audience.