ASHINGTON, March 31 � Governors of both parties appealed to Congress on Wednesday to pass a five-year extension of the 1996 welfare law, even as the Senate was caught up in growing partisan conflict over Democrats' demands that the measure include an increase in the minimum wage.

In a letter to the Senate, governors said passage of a five-year reauthorization was essential to "provide states with the predictability needed for continued success of welfare reform initiatives across the country."

Governors were instrumental in securing passage of the 1996 law, which broke with 60 years of social welfare policy and gave states vast discretion to run their welfare programs with lump sums of federal money. Since then, the number of people on welfare has dropped 60 percent, to 4.9 million.

Gov. John Hoeven of North Dakota, a Republican, and Gov. Jennifer M. Granholm of Michigan, a Democrat, told Congress that reaching agreement on welfare was an urgent priority. They wrote on behalf of the National Governors Association.

Some lawmakers have suggested that Congress could keep renewing welfare programs for three months at a time, but governors said that would be a big mistake.

Wade F. Horn, assistant secretary of health and human services in charge of welfare policy, said "it would be tragic" if Congress did not renew the 1996 law. "States are clamoring to know the rules under which they will be operating for the next five years," Mr. Horn said.

State welfare officials said they were delighted that the Senate voted overwhelmingly on Tuesday to increase spending on child care for welfare recipients and other low-income families. But they expressed concern that the bill could become bogged down in an election-year struggle between Republicans and Democrats in the Senate.

Democrats like the provision of the bill that would add $7 billion to child care programs over the next five years. "This is a huge victory for New York's families," said Senator Hillary Rodham Clinton of New York. But Democrats also insisted that the Senate vote on amendments dealing with the minimum wage, overtime pay, jobless benefits and other issues not technically germane to the welfare legislation.

Senator John B. Breaux of Louisiana, a moderate Democrat, said, "There's basic agreement on the core principles of the welfare bill, but I am becoming very concerned that these ancillary issues could prevent the bill from passing in the Senate."

The administration has opposed the $7 billion increase in child care, saying it is not needed. The House bill provides a $1 billion increase in automatic, or mandatory, spending for child care.

Senate Republicans said they would, at some point, make a deal with the Democrats to allow a vote on the minimum wage. But they want certain assurances in return, to guarantee a final Senate vote on the welfare bill and to clear the way for negotiations with the House, which passed its version of the legislation in February 2003.

Lacking an agreement on how to proceed, the Senate majority leader, Bill Frist, Republican of Tennessee, filed a motion to limit debate and amendments on the welfare bill. It takes 60 votes to approve such a motion.

Dr. Frist said Democrats were endangering the welfare legislation, which he said could help millions of people escape poverty by moving from welfare to work. Senator Rick Santorum, Republican of Pennsylvania, said that while he could support some increase in the minimum wage, he believed that "welfare reform is being blocked by the obstructionist tactics of the Democrats."

Democrats said their proposal, to raise the minimum wage to $7 an hour, from $5.15, over two years, was relevant to the welfare bill because many welfare recipients take jobs at or near that level. Senator Christopher J. Dodd, Democrat of Connecticut, said Congress had received six raises since the minimum wage was last increased in 1997.

Moreover, Democrats asserted that a significant number of Republican senators opposed a substantial increase in the minimum wage but wanted to avoid the political risks of voting against it in an election year.