The Pentagon has taken the first step toward asking Congress to restore some of the money that lawmakers are still cutting from the fiscal 1986 defense budget, Reagan administration officials said yesterday.

Defense Secretary Caspar W. Weinberger directed the Pentagon's comptroller this week to alert the armed services to the possibility that President Reagan may ask for supplemental funds, officials said.

This activity, though preliminary, is likely to anger Senate Majority Leader Robert J. Dole (R-Kan.) further. He said yesterday that Congress did not cut the Pentagon budget deeply enough this year and would be tougher next time around.

No dollar amounts or list of projects have been established for the possible appeal, according to the Pentagon, but the services are assessing the cuts' impact and considering what deleted projects they most want saved if Reagan goes ahead with a supplemental request.

Army officials said they are assuming that cuts reducing readiness to fight a conventional war would be appealed first. They said they doubt that Weinberger or Reagan would use a supplemental request to try to restore reductions in such strategic nuclear programs as that involving the MX missile.

The Senate has approved a "pause" in MX deployment at 50 missiles in Minuteman missile silos, while the House has voted for a cap of 40 MXs. The difference is under debate in a House-Senate conference on rival fiscal 1986 defense authorization bills.

In confirming preliminary action on the possible supplemental request, one Pentagon official said Weinberger, going along with the compromise defense budget worked out between Reagan and Dole earlier this year, had assurances that a request for extra money would be justified if cuts significantly degraded military readiness.

If a military supplemental request is put together by the Pentagon and White House, it could be submitted later in this congressional session or be held until next year. The fiscal year at issue runs from Oct. 1, 1985, to Sept. 30, 1986.

The House and Senate are still struggling over money ceilings in military and domestic programs for fiscal 1986.

The delicate compromise forged with Reagan's help gives the Pentagon budget authorization, as distinguished from actual spending, to grow only enough between fiscal 1985 and 1986 to cover inflation. Congressional staff participating in the negotiations said yesterday that the Pentagon would be foolish to make any requests for extra funds now.

Neither the defense nor domestic budgets will be cut enough this year to reduce the federal deficit significantly, congressional budget specialists predict. They said that lawmakers would face a $200 billion deficit next year and be even more inclined to cut defense spending in 1986 than they were this year.

Reagan has a second avenue available to him to ask Congress for extra money for military programs this year. In announcing his decision to abide by the missile launcher limits in the unratified SALT II arms treaty, the president said that if the Soviet Union continues to violate the treaty, he might accelerate U.S. strategic programs in November.

Such action would require more money than is contained in the defense budget now in conference.