Responding to the sinking dollar, the Federal Reserve Board moved yesterday to tighten interest rates another notch.

The increase in the Fed's target rates for federal funds from 7-7/8 percent to 8 percent came as President Carter and Fed Chairman G. William Miller expressed renewed concern about the dollar. Their statment helped the dollar rally and sent stocks higher but also sent treasury bill rates soaring to their highest levels in weeks.

"The dollar has taken the forefront again, and it's overrunning domestic considerations" in formulating monetary policy, commented Thomas Bell, an analyst with Merill Lynch Government Securities.

The tightening action is the first in nearly a month and comes at a time when many money market analysts had thought that interest rates may have peaked for the current cycle.

But Bell and other analysts predicted that the Fed in the next few days will follow yesterday's tightening of credit market conditions with another step - an increase in the discount rate, the money the Fed charges its own member banks for loans.

It is highly unusual for the Fed to raise interest rates in response to international rather than domestic economic conditions.

However, the nation's central bank did just that in early January of this year when it increased the discount rate one-half point to 6.5 percent in response to a plunging dollar and managed to stem the decline for several weeks. At the same time it sent domestic short-term rates spurting.

Currently at 7.25 percent, most analysts expected the next increase by the Fed will raise the discount rate to 7.75 percent.

A quarter-point increase, like the one initiated in early July would have little positive impact, "and could hurt rather than help the dollar," said Lawrence Kudlow, chief monetary economist for Paine Webber Fixed Income Investments.

Kudlow explained that a quarterpoint jump would be considered too small, and that even a half-point gain would quickly be dismissed as symbolic by currency traders if this was not accompanied by a parallel move to cut down on the growth of reserves in the banking system which he believes has been fueling inflation.

There are two main reasons why higher interest rates help the dollar.

First, a higher level of rates tends to attract funds from abroad into U.S. fixed income investments, thus sopping up dollars.

Second, a tightening move signals a more serious attitude toward fighting inflation.And the recent double-digit pace of inflation in the U.S., relative to the rate in other countries, has significantly added to the dollar's weakness in currency markets.

At the same time, there is concern that has been voiced by Fed Chairman Miller among others that a continued rise in interest rates could choke off the current U.S. economic recovery.

Yesterday's increase in the federa1 funds rate - which banks charge each other for overnight loans and which the Fed uses as a target for its money market operations - came a day after the regular monthly meeting of the Fed's Open Market Committee which sets monetary policy.

However, the market's confirmation that the Fed had raised its target to 8 percent did not come until after a morning White House meeting on the dollar with Miller in attendance.

Following that meeting, President Carter expressed "deep concern" and Miller was said to be "considering what might be done" about the dollar's slide and would report back.

Shortly afterward, when the federal funds rate had pushed up to 8 percent, the Fed came into the market to do some repurchases for customers, signalling that it would tolerate the new 8 percent level. (At the beginning of the 1978, the federal funds rate was just over 6.5 percent.)

The sequence of events led some analysts to speculate that the decision to tighten was first cleared with the White House.

"It appears Miller didn't want to act without the White House meeting," commented one analyst. "I would prefer to see the Fed taking a more independent course instead of dragging its feet and waiting for broad support from the administration. The Fed should have taken action with respect to the dollar two weeks ago when the price of gold shot above $200 and the dollar collapsed following the Bonn summit."