The House Appropriations Committee yesterday rescued the Federal Trade Commission from a possible shutdown this weekend as it approved a 45-day extension of the agency's temporary funding.

The FTC's spending authority runs out tomorrow, the latest in a series of money cutoff deadlines that Congress imposed on itself to speed settlement of a three-year dispute over the controversial regulatory agency's powers.

But, encouraged by the committee's action, the commission notified its 1,700 employes to come to work as usual next week, even though the money won't officially be in hand until the new interim funding bill is approved by the House and Senate. Approval by the two houses is expected sometime next week, according to congressional sources.

Even though the money continues to flow, however, the FTC's problems will be far from over.

The 45-day extension was designed to give House and Senate conferees time to resolve their differences over commission's powers. Both chambers have approved by legislation curbing the FTC's authority to impose consumer protection rules on private businesses, but the bills differ sharply.

The conferees held their first meeting yesterday but failed to agree on anything more than an appeal to House and Senate to give prompt approval to the interim money bill.

When discussion turned to the issue of a one-house congressional veto of FTC rules, which the House is demanding over strong opposition from the Senate, Rep. Harley O. Staggers (D-W.Va.), chairman of the conference committee, diplomatically adjourned the meeting. The conferees will not meet again until March 26 to consider staff-drafted proposals for compromise.

Along with the one-house veto, the House Bill would keep the FTC from regulating the funeral industry and agricultural cooperatives such as Sunkist Growers Inc., which it has been investigating for two years. The Senate bill contains a milder two-house legislative review procedure but would ban proceedings involving children's advertising on television, used car sales, the insurance industry and industry groups that set voluntary product standards.

When Sen. Wendell H. Ford (D-Ky.) suggested that the one-house veto issue be put off to the last, Rep. James H. Scheuer (D-N.Y.) objected strongly, saying there would be no bill without a veto provision. If a veto was the only issue, "then we can quit now," retorted Ford.

The exchange did not appear to bode well for a compromise advanced earlier in the day by Rep. Richard L. Ottinger (D-N.Y.), who proposed a two-house legislative review procedure with safeguards for assuring prompt action. He would drop the one-house veto and all the single-industry provisions.

Ottinger's proposal was endorsed by many consumer groups and appears to meet Carter administration objections to both the Senate and House bills, but it would require a sharp reversal of the anti-FTC tide in Congress to win approval.

The interim funding bill makes no changes in existing restrictions on the FTC, which bar new investigations and rule making by the agency until its powers are clarified. The Appropriations Committee rejected a proposal to add additional curbs contemplated by the Senate and House bills.

One possible hitch to passage of the funding measure is the current moratorium on any new spending bills that was triggered when Congress exceeded its fiscal 1980 budget ceiling earlier this month. But legislative leaders were working yesterday on ways of circumventing the spending ban and expressed optimism that a way could be found.