The Dow Jones Industrial Average was up 26.3 points at 13,104, with 20 of its 30 components trading higher.
The S&P 500 rose 1.3 points to 1,447, and the Nasdaq Composite rose 3.1 points to 2,508.
"While there still may be some upside left to this 'relief' rally, we are more like to move money to the sidelines than buy equities," said Paul Nolte, director of Investments at Hinsdale Associates.
"The book is a long way from being closed to the debt issues in the U.S.," he wrote in a note.
The Fed moved to reassure investors Friday by cutting its discount rate, the interest in charges on its loans to banks, by a half-point to 5.75%, and said it stands ready to do more. U.S. stocks jumped in response, with the Dow industrials climbing 233 points, the Nasdaq Composite up 53 points and the S&P 500 adding 34 points.
Sharp gains were also seen in Asian and European markets.
"Markets probably have passed the point of maximum stress, at least in this episode," said Gerard Minack, a strategist for Morgan Stanley in Australia. He said the Fed was pressed to act by the near shutdown of short-term funding in the asset-backed commercial paper market.
The yen fell against rivals, after gains last week as investors backed off risky trades. The dollar rose 0.8% at 115.18 yen.
Yields on 10-year Treasury notes edged up to 4.68%.
Shares of Countrywide Financial gained 4%, after slumping 31% last week. The nation's largest mortgage lender has started laying workers involved in originating loans as part of an effort to weather a credit crunch, The Wall Street Journal reported.
Among Dow components, American Express Co. gained 0.4% after London's Sunday Times reported the company had put its private banking business on the block.
Elsewhere, J.P Morgan downgraded The McGraw-Hill Cos., the parent of credit-rating agency Standard & Poor's to neutral from overweight, citing signs the credit market would see a meaningful drop in issuance activity.
HSBC Holdings PLC said it is in talks to acquire a majority of Korea Exchange Bank from Lone Star Funds.
In other early action, shares of CDC Corp. rose 0.6% after the provider of software, Internet and mobile communications services said it would register with the Securities and Exchange Commission an initial public offering of as much as $225 million of Class A common shares.
Lowe's Cos.'s climbed 6% up after the home improvement retailer reported second-quarter net income increased 9% from a year earlier to $1.02 billion, or 67 cents a share.
By Kate Gibson