The nation's money supply unexpectedly rose by $700 million in the week ending Jan. 13, after soaring by $10.2 billion in the first week of the year.

Money markets, which had been hoping for a large fall in money, reacted immediately with higher interest rates. Taxable bonds dropped one point, corporate bonds were also marked down and Treasury securities fell more than a point. Several analysts said further interest rate rises are likely next week because the Federal Reserve is expected to tighten credit in response to the money surge.

In the last two to three months, money growth has accelerated rapidly, and apparently inexplicably. During a recession it is normal to have sluggish money growth as both business and individuals cut back their credit demands. Although senior Federal Reserve officials say they are puzzled by the upsurge, they are likely to respond anyway rather than wait to see whether the rise continues.

However, if they move to a more restrictive policy, it is likely to send interest rates higher and threaten to deepen the present recession. Although President Reagan this week blamed a recent climb in interest rates on the money surge, most analysts believe that tighter money will lead to higher--not lower--rates.

The interest rate climb was also surprising, economists say.

Rates are "extraordinarily high" for this stage of the business cycle, Nobel Prize winner James Tobin said this week. Analysts believe that further rises could mean that the economy does not pick up in the next few months as the administration has predicted it will.

The Fed already has moved toward a slightly tighter policy, according to some market analysts. Under their operating procedures, they automatically tighten up if money growth exceeds targets, but they may have tempered this reaction in recent weeks because of the uncertainty over why money was growing so fast, economists said.

The M-1 money measure--which includes currency in circulation and all checking accounts at financial institutions--rose to a seasonally adjusted $451.3 billion in the week ending Jan. 13, the Fed reported. At the end of the previous week, M-1 stood at $450.6 billion, up from the $450.2 billion originally reported.

For the latest four weeks, M1 averaged $446 billion, a 12.6 percent annualized rate of increase from three months earlier.

However, commercial and industrial loans at major New York city banks fell by $613 million in the week ending Jan. 13, the New York Federal Reserve Bank reported yeterday. In the previous week, there was a drop of $353 million.

Meanwhile yesterday, the government raised the ceiling rate on government-backed mortgages to 16 1/2 percent from 15 1/2 percent effective Monday.