Congress was officially asked by the Reagan administration yesterday to let the national debt rise past a trillion dollars in the near future.

The bad news came from Assistant Treasury Secretary Roger W. Mehle, who urged the Senate Finance Committee, at a hearing before its subcommittee on taxation and debt management, to approve House-passed legislation raising the nation's legal debt limit to $1.079 trillion for fiscal 1982.

With the government expected to bump up against the current ceiling of $985 billion by the end of the month, prompt action is necessary or the "Treasury will run out of cash altogether in the first week of October," Mehle warned.

The symbolism of a trillion-dollar debt is especially distasteful to congressional conservatives, many of whom have built their careers partly on opposition to rising national debts.

But it is now their administration that is requesting the debt ceiling boost--actually its second increase since President Reagan took office nine months ago--and warning of the dire consequences of delay or obstruction.

Although the debt bill was earlier suggested by House and Senate Republican leaders as a vehicle for giving Reagan the power to cut spending by impounding appropriated funds, Mehle did not propose such a course. He said his only concern was "timely passage" of the debt ceiling bill.

"I think it the impoundment proposal is dead," said subcommittee chairman Bob Packwood (R-Ore.), confirming other Senate Republican leaders' assessments that the prospect of impoundment, which was last used by former president Nixon, has aroused such adverse reactions that its chances of resurrection by Congress are minimal.

Congress also must deal in the near future with an interim funding measure for those agencies that will be without fresh appropriations bills when the new fiscal year begins Oct. 1. Most departments fall in this category. In this continuing resolution Congress may be asked to take action on the new set of spending cut proposals that the administration is expected to announce next week.

In addition to pushing for impoundment, House Minority Leader Robert H. Michel (R-Ill.) has been talking about a 10 percent across-the-board cut in non-entitlement programs, or some modification depending on what Reagan recommends in the way of Pentagon cutbacks, in the stopgap money bill. He would also have the continuing resolution run all the way through March 31, rather than just for the usual one or two months.

But no decisions are expected until after Reagan decides what to cut, presumably by the middle of next week. After telling Cabinet members Thursday that they will have to cut up to $74 billion in 1983 and 1984, and even more than the $35 billion already slashed from spending for 1982, Reagan took off by midafternoon yesterday for a weekend at Camp David. Aides said he was expected to review briefing papers during the stay.

Finance Committee approval of the debt measure is expected Tuesday, without any reference to impoundment, according to Packwood. However, attempts may be made to add impoundment on the Senate floor.

Meanwhile, a Senate Appropriations subcommittee approved a House-passed money bill covering the State, Justice and Commerce departments after striking out extraneous House riders, including those that would ban use of funds to keep prayers out of public schools as well as restrictions on the activities of the Legal Services Corp.

The subcommittee also rejected a proposal to reduce funding for the legal services agency from $241 million to $100 million.