House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) yesterday agreed to postpone a vote on the MX missile until after the July 4 recess at the request of liberals who want President Reagan to explain his new arms control proposals further.

Liberal Democrats who oppose the MX, led by Massachusetts Reps. Nicholas Mavroules and Edward J. Markey, persuaded O'Neill and Armed Services Committee Chairman Melvin Price (D-Ill.) to make the MX the last major item of consideration in the defense authorization bill.

Work on the bill, which is being handled by Price, is scheduled to begin next week.

Thirty or 40 House Democrats met Wednesday night and agreed to endorse the postponement Mavroules had been seeking earlier in the week.

President Reagan won key victories last month when the House and Senate agreed to release an estimated $625 million for full-scale engineering and development of the giant, 10-warhead MX intercontinental nuclear weapon.

Meanwhile, the House Appropriations Committee approved a $7.05 billion bill to finance military construction and family housing projects in the fiscal year starting Oct. 1.

The measure, cleared by voice vote yesterday after brief discussion, is $1.6 billion smaller than Reagan had sought and $171.2 million below the fiscal 1983 level. It prompted a letter of protest from Office of Management and Budget Director David A. Stockman that the cuts had been too deep.

Sponsors said the biggest single chunk--$450 million--was cut because the admininistration changed its plans to deploy the MX missile in new "Dense Pack" silos and place them instead in existing Minuteman III silos. Some $30 million in planning and design funds was retained for the weapons program.

The panel also deleted all $96.4 million the Pentagon had earmarked for construction of a base at Ras Banas on the Red Sea in Egypt for use by U.S. forces that would be rushed to the Middle East in case of a crisis.

U.S.-Egyptian negotiations on who would control construction of the base fell through recently, and the Cairo government is going ahead with the project with its own money, said Rep. W.G. (Bill) Hefner (D-N.C.), chairman of the military construction subcommittee.