The dollar rallied on the foreign exchange markets yesterday in response to Friday's Federal Reserve Board action raising domestic interest rates - providing an encouraging initial reaction to the latest U.S. efforts to reverse the recent slide.

The U.S. currency began climbing visibly at the start of trading in most major world financial centers and, after peaking in mid-day, closed generally at a slightly higher level that it recorded late last week.

Analysts cautioned that it was "still premature" to say the dollar's slide had been arrested, and it may be several more days before the full impact of the Fed's action is known. Some dealers were reported still skeptical about the U.S. commitment to support the dollar.

However, observers noted that if the dollar had not rebounded yesterday, it would have meant the U.S. currency was far more deeply in trouble than expected, and that massive intervention would be needed to break the latest slide.

The strengthening yesterday was aided by two separate actions that, taken together, tended to bolster the Fed's move Friday in raising the discount rate:

Early in the trading day, the West German central bank entered the market visibly to support the dollar - a modest, but nevertheless important step that provided a strong psychological boost to the previous U.S. efforts to prop the dollar up.

Later, the Federal Reserve Board backed up its Friday action by absorbing funds in the New York money markets, sending interest rates up. The key federal funds rate - the interest on overnight loans to banks - rose to 6.9/16 per cent, from 6 1/2 per cent last week.

The action came as central bankers from the U.S. Japan and Europe met privately in Basle, Switzerland, to discuss the currency situation - reportedly making "progress" in developing a common strategy to help reverse the dollar's decline.

Although the U.S. reportedly came under pressure to take steps to slow its oil imports, which many consider the major reason behind the dollar's slide recently, the Fed's Friday action apparently was hailed as a welcome step.

Arthur F. Burns, retiring chairman of the Federal Reserve Board, who represented the U.S. at the session, declined to elaborate on the discussions.

The move by the Fed yesterday in absorbing funds in the New York money markets was regarded as a key step to back up its Friday action. On Friday, the Fed raised the discount rate - the interest it charges on loans to member banks - to 6 1/2 per cent, from 6 per cent before.

The measure on Friday was intended to show the markets that the U.S. was serious about defending the dollar against the recent attack - even to the point of raising domestic interest rates, if necessary. It was only the fifth such move in the past 15 years.

However, analysts said many traders had been skeptical because the discount rate increase alone was not enough to boost domestic interest rates very much. Yesterday's draining off to funds from the money markets, they said, tended to bolster the Fed's credibility.

Trading was mixed at the major foreign currency centers. In frankfort, the dollar climbed to 2.15 marks in early morning before finally settling back to 2,1445 marks near close - up 1.4 pfening from late Friday. The pound fell 1.125 cents from last week's level.

The impact was modest in Tokyo, with the dollar closing at 241.875 yen, up from 240.825 Friday. Volume was low on virtually all the major exchanges.

The U.S. move to stem the dollar's slide is a recent phenomenon. Until a few weeks ago, official policy had been to let the dollar decline, purposely, to help out pressure on the West Germans and Japanese to stimulate their economies.

Meanwhile, reaction continued to be mixed in the Carter administration over Friday's Fed announcement. While White House officials agree it's time to halt the decline of the dollar, they also are reluctant to see domestic interest rates go up, for fear of slowing the economy.