WASHINGTON (AP) _ The State Department's No. 2 officer on Saturday denounced Poland's crackdown on strikers and said U.S. backing for that government's economic recovery plan will remain frozen until the program wins popular support.

''We have to condemn the violence, imprisonments, the beatings that are reported to be taking place,'' Deputy Secretary of State John C. Whitehead said. ''The situation there is very sad.''

Whitehead also said that during a trip to Algeria this week he will urge leaders to see that the hijackers of a Kuwaiti airliner, who might still be in Algeria, are ''brought to justice.''

U.S. officials disclosed earlier last week that U.S. support for Poland's economic programs would flag unless the Polish government resumes a dialogue with labor groups, but in an interview with three reporters, Whitehead defined the U.S. position with greater detail and clarity.

Since lifting sanctions in 1986, the United States has been cautiously encouraging economic recovery in Poland and has pledged to support Warsaw's plea for assistance from international financial institutions.

Whitehead said the Polish program - which includes wage and price austerity - would never be effective without popular support. He said that must be achieved through consultations with workers, notably the Solidarity free trade movement that is leading the current strikes.

''We are urging the government to establish a dialogue with the workers of Poland, including members of Solidarity'' to create an ''enthusiasm'' for the program, he said.

''We believe until that happens that the economic program of the government, which strikes us as being a basically sensible program, will not be able to become effective,'' he said. As a result, ''the ability of the United States to support that program will be ruined.''

He said the United States had been planning to back Poland's applications for loans from the World Bank and to work with the so-called ''Paris Club'' of lender nations to restructure Poland's massive foreign debt.

There also is a possibility of direct U.S. assistance, Whitehead said.

''But all of those things are now in jeopardy because of the lack of a kind of national reconciliation,'' Whitehead said.

Asked why Poland acted so strenuously against the strikers, knowing the United States would react strongly, Whitehead said ''the Polish government evidently feels that it can impose an economic program on the country without any kind of participation of the people in developing the program.

''We have felt all along it is not possible to do it that way and now the evidence begins to appear that it is not possible,'' he said.

Whitehead's visit to Poland last year was the highest-ranking State Department mission to that country since the martial law crackdown against Solidarity in 1981, and he has been to other Eastern European countries as the Reagan administration official with special responsibility for relations with the Soviet bloc nations.

During his visits, he has told leaders that improved performance on human rights and moves toward freer economic life will lead to the closer commercial ties they have been seeking with the United States.

Whitehead is scheduled on Monday to begin a 12-day trip to Morocco, Tunisia, Algeria and France.

In Algeria, he said, he would seek more information from the government on its role in the ending of last month's Kuwaiti Air Lines hijacking. The plane, captured by gunmen seeking the release of Shiite Moslems imprisoned on terrorism charges in Kuwait, ended up in Algiers, where authorities talked the hijackers into freeing the passengers.

There have been unconfirmed published reports that the hijackers are still in Algeria but Whitehead said ''we don't know for sure.''

He repeated U.S. pleas to Algeria - and any other country where the hijackers might be - to arrest them.

''We will set forth our views strongly, that hijackers should not be allowed to get away with their criminal acts and must be brought to justice,'' Whitehead said.