Both Democratic and Republican leaders in the House indicated yesterday that they will not rush to approve the administration's latest preferred version of a money bill to finance some government operations this summer.

Irritated at having been ignored in the rewriting of a supplemental appropriations bill, Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) and Minority Leader Robert H. Michel (R-Ill.) got together a joint statement promising only to try to resolve the dispute "as soon as possible."

That meant, aides in the Capitol said, that there would be no House action on the full-Senate-passed $5.3 billion 1982 supplemental until Congress reconvenes July 12, a decision that could require a modest curtailment of some agencies' operations in the interim.

The Senate Tuesday ratified a compromise worked out by Republican leaders and budget director David A. Stockman after Stockman hinted at another presidential veto--the third in one week--if Congress sent down a different version that the House had passed just before going on vacation.

Michel was described by associates yesterday as "frustrated" by the White House veto threat against that measure and upset because he was not consulted in Stockman's deliberations. He had felt assured that President Reagan would sign the earlier version, aides said.

According to the Office of Management and Budget, failure of the House to act this week could mean partial furloughing of about 1,240 employes at the end of this week in the Merit Systems Protection Board and the inspector general's office of the Department of Health and Human Services.

The House, which is in pro forma session today, may be asked to pass a special supplemental to prevent furloughs in the HHS offices, House aides said.