Health, Education and Welfare Secretary Joseph A. Califano Jr. yesterday convened a new Social Security advisory council that will recommend some solutions next year to the problems facing the giant system, including whether to raise the normal retirement age beyond 65.

Califano, in opening remarks, also urged the council to consider such issues as the costly expansion of the disability rolls, alleged discrimination against women in Social Security, and demands that federal employes be included in the system.

Califano told the 13-member group in addition that it should explore ways to finance Social Security, which now has 34 million beneficiaries and costs $100 billion a year.

Meanwhile, Senate Social Security subcommittee Chairman Gaylord Nelson (D-Wis.) and Rep. Abner J. Mikva (D-III.) met with President Carter yesterday to discuss the congressional drive to freeze impending Social Security tax increases and make up the loss by putting Treasury General revenue into the Social Security hospital insurrance system.

The President has been opposing this idea but Nelson and Mikva, who favor it, said they thought it would be wise if he had some contingency proposal to mesh a Social Security rollback with his tax cut bill. The House Democratic caucus voted 150 to 57 this week to endorse a tax freeze and general revenue use for part of the costs of Social Security.

Califano, calling Social Security the most important social program in the government, said the council, which was sworn in yesterday, should find solutions to these vexing issues:

Whether housewives should be given some form of Social Security coverage for disability and old-age insurance, even though they do not work in employment subject to the Social Security tax. Some women's groups have suggested "homemaker credits" or giving a housewife credit for part of her husband's Social Security tax payments.

Whether (and how) the federal employe pension system and state and local government pension systems should be intergrated into Social Security. Most federal employe unions believe federal workers would be sorse off under Social Security and have strongly resisted any intergration.

Whether, as the population ages, the basic retirement age under Social Security should be raised to 67, 68 or some other figure, a change that could save substantial amounts of money.

Whether the cash-benefit system is adequate, and whether it should be reduced for some groups of workers and increased for others. Under last year's law, the average worker on retiring will get monthly benefits equal to 43 percent of his Social Security-taxed earnings in the last year before retirement. However, the highest-paid workers will get a "replacement ratio" of 25 to 29 percent, while the lowest paid will get about 56 percent. Should these ratios be changed? Should benefits be raised all along the line enough to obviate the need for some types of private pensions?

IS the disability insurance program under Social Security the best way to support long-term disabled workers? Is it too easy to get benefits under that program now,leading to swollen benefit rolls?

The new council is headed by Stanford G. Ross, a member of the law firm of Caplin and Drysdale and former general counsel of the Department of Transportation. It is to issue its recommendations by Oct. 1, 1979.

It includes economists Gardner Ackley and Joseph A. Pechman, Trans Union Corp. president J.W. Van Gorkom, Equitable Life Executive Vice President Morton Million, former Social Security Commissioner Robert M. Ball and other labor, academic and business figures.