The congressional push for recession relief picked up speed yesterday as a House Ways and Means subcommittee approved up to 10 more weeks of supplemental unemployment benefits through Sept. 30 for more than 1 million jobless workers who have exhausted their existing assistance.

The Democratic-controlled subcommittee on public assistance and unemployment compensation approved the added benefits after rejecting, 7 to 4, on a party-line vote, a Reagan administration proposal for a simple nine-month extension of the existing program, giving jobless workers up to 55 weeks of benefits.

The proposed change, which is expected to be approved by the full committee and embraced by the Democratic leadership, would provide as much as 65 weeks of benefits for unemployed workers in areas that are hardest hit by the recession, although most would receive less.

Workers who have not exhausted all their current benefits by April 1, the starting date for the new program, would qualify for extra weeks of assistance depending on how long their existing entitlements last, the total not to exceed 65 weeks.

As many as 1.8 million workers--1.2 million who will be off the unemployment assistance rolls by April 1 and 600,000 who would drop off before Sept. 30--would receive varying amounts of additional assistance.

The subcommittee's proposal would cost $2.6 billion, according to Congressional Budget Office estimates, or up to $3.3 billion under Department of Labor calculations, compared with a $1.8 billion estimate for the administration's proposal over the same period.

The party-line vote in the subcommittee indicated that partisan differences will continue as the administration and House Democrats try to put together a jobs package.

Moreover, House Majority Leader James C. Wright Jr. (D-Tex.) signaled yesterday that the Democrats, despite warnings from Republican leaders against "tinkering," intend to add to Reagan's $4.3 billion proposal, which was made last week in response to bipartisan demands for immediate action on jobs.

Meanwhile, Republican as well as Democratic members of the Senate Labor and Human Resources subcommittee on employment took issue with presidential economic adviser Martin Feldstein over administration job-creating proposals.

And Feldstein, asserting that "economic recovery is by far the best jobs program," took a dim view of congressional proposals for public service jobs, including one advanced by subcommittee chairman Dan Quayle (R-Ind.).

Quayle, in turn, suggested that the administration's program would be improved by inclusion of some public service jobs, which he said can provide more employment more quickly than construction jobs.

Feldstein defended the administration's inclusion of accelerated spending for construction work in its $4.3 billion jobs offer, saying that the time to do such work is when, as now, the economy is slack.

But, he insisted, "it must be made very clear to the financial markets and others that advancing the date of future outlays does not mean an increase in cumulative government spending . . . . "

Sen. Edward M. Kennedy (D-Mass.), who yesterday introduced a $7.3 billion jobs program for the next two years, was critical of the administration's offer, as was Sen. Howard M. Metzenbaum (D-Ohio), who said, "If that's all we do, it'll be too little too late."

If administration officials are willing only to accelerate construction jobs, "they'll not only have opposition from Democrats but they'll have opposition from Republicans too," said Quayle.

In a bill co-sponsored by Labor and Human Resources Committee Chairman Orrin G. Hatch (R-Utah), Quayle has proposed $2 billion for public service and other "labor-intensive" jobs, $100 million on top of the $240 million that the administration has proposed for job retraining, and a variety of other retraining and hiring incentives.

Without provisions of this sort in the $4.3 billion measure, the administration faces follow-up legislation that may be more than it wants, Quayle warned.