The United States, pointing to an increased movement of Soviet advisers and military equipment into Afghanistan, yesterday warned the Soviet Union against interfering in fighting currently going on in that country between rebels and government forces.

At the same time, State Department spokesman Hodding Carter III rejected charges in the Soviet press that the United States is aiding Afghan insurgents.

"The United States has not interfered in the internal affairs of Afghanistan," said Carter after reading the statement warning the Soviets against taking part in the fighting.

Carter's statement appeared to be a diplomatic exercise, telling the Soviets that the United States resents charges against it at a time when the Russians are getting even more deeply involved in Afghanistan.

"When the pot is spending a great deal of time describing supposed activities by the kettle, it might at least be worth noting that the pot is vigorously boiling -- and in this case, that is what is going on," said a State Department official, explaining the timing of Carter's statement.

Western diplomatic sources in Moscow said the United States protested to the Soviet Foreign Ministry over Russian radio and newspaper charges that America was training antigovernment rebels in Afghanistan. Reuter reported that the protest was made Wednesday, when U.S. diplomats told the Soviets the charges could endanger American lives.

Carter's statement here yesterday was one more sign of American sensitivity to the increased Soviet maneuvering in a wide are a stretching from the Horn of Africa, through Yemen to Afghanistan, where the pro-Soviet government of President Nur Mohammed Taraki took power in a bloody coup almost a year ago.

The State Department spokesman said there has been "a substantial increase" in the number of Soviet flights into Afghanistan in the past few days as well as an "accelerated delivery" of military equipment to the Taraki government.

Over the past several months, Carter continued, the Soviets have increased the number of military advisers there until they have now reached about 1,000.

But, he said, there is no indication that the Soviets have taken a combat role in fighting between the government and rebel tribesman -- many of them, Shiite Moslems fearful the pro-Russian government will curtail religious freedom -- that is now going on in both eastern and western sections of the country.

Carter said American officials have little information about the fighting in Afghanistan. They still have no knowledge about five American missionaries working in an eye hospital in the city of Herat -- located where the borders of Iran, Afghanistan and the Soviet Union meet -- since the telephone lines have been cut for a week. There are conflicting reports as to whether the rebels or the government control Herat.

Despite fighting elsewhere in Afghanistan, all is quiet in the capital city of Kabul, Carter said.

Merely supplying aid to Afghanistan is not enough to constitute Soviet interference in its external affairs, Carter said

But without defining what interference would be, he added, "We would regard external involvement in Afghanistan's internal problems as a serious matter with a potential for heightening tensions and destabilizing the situation in the entire region."

Relations between the United States and the Soviet Union over Afghanistan hit a low point when the American ambassador in Kabul, Adolph (Spike) Dubs was killed last month when Afghan police stormed a room in which he was being held by terrorists.

The State Department charged that Soviets were advising the Afghan police during the incident, and demanded a detailed account from both the Afghan and Soviet governments. Carter said no such account has been received, and the United States is not actively considering finding a replacement for Dubs.

The internal battles in Afghanistan have sparked charges that both Pakistan and Iran were aiding rebel forces. Both neighboring nations have denied the charges, and Thursday Iran expelled the Afghan charge d' affairs from Tehran in retaliation for a similar expulsion of the Iranian consul in Herat.