The State Department said yesterday that negotiations for a new strategic arms limitation treaty (SALT) are "moving ahead" and said the United States looks forward to an early summit signing "in this country."

The statement by spokesman Ken Brown gave no status report on the remaining issues, which are reported to include the definition of the one new land-based intercontinental missile permitted for each side under the proposed treaty, and problems concerning Soviet practices that impede verification.

Administration sources expressed belief that the outstanding questions could be resolved quickly, if the two sides have the will to do so. Secretary of State Cyrus R. Vance met Soviet Ambassador Anatoliy F. Dobrynin Tuesday to give U.S. responses to Soviet compromise proposals presented last week. With President Carter, Vance and other top U.S. officials on the way to the Middle East for negotiations with Egypt and Israel, the ball is considered to be in the Soviet court for at least the rest of this week.

Brown's statement regarding the location of the summit puts on the record in a more determined way than before U.S. insistence that a summit meeting between Carter and Soviet President Leonid Brezhnev take place somewhere in the United States. White House political aides are reported to argue that Carter's prestige would be diminished if he agrees to meet Brezhnev in Moscow or Geneva, as the Soviets evidently prefer.

The United States reportedly has suggested Alaska or Hawaii for the summit if Brezhnev is determined not to come to Washington. In American eyes, it is uncertain whether Brezhnev's reluctance to come here is due to his health or to political reasons.

China's announcement and troop movements toward withdrawal from Vietnam are believed to clear away a potential obstacle to a new SALT agreement. Some high U.S. officials believed it was unlikely that the Soviet Union would conclude a treaty with the United States while China's invasion kept superpower tensions high.

On the other hand, a developing Washington-Moscow quarrel regarding Yemen could become an issue of magnitude enough to cause new problems for completion of the SALT process.