Secretary of State George P. Shultz, carrying Middle East peace proposals, arrived in the Syrian capital Tuesday to a critical reception after an indecisive meeting with King Hussein of Jordan.

Shultz came to Damascus from Amman as a semi-official Syrian paper asked: "What is the use of this tour?"The English-language Syria Times said Shultz's proposal for limited Palestinian self-rule in Israeli-occupied territories ignored "the inalienable rights of the Arab people of Palestine."

That reflected a serious challenge from Syria, Moscow's main Arab ally, to Shultz's blueprint for a Middle East peace plan. In Damascus, Shultz is to meet with President Hafez Assad.

In Amman, Shultz met with King Hussein for 90 minutes and State Department spokesman Charles E. Redman said they had a "useful, thoughtful discussion."

Asked if there was any change in Shultz's statement that neither Israel nor Arab nations had made any commitment to Washington's latest blueprint for a Middle East peace plan, he said: "Nothing has changed on that."

He said that Hussein had insisted on an international peace conference as the only way to achieve a Middle East peace settlement.

Monday, Shultz met with Israeli leaders.

"We do have a sense of movement," a senior U.S. official said in Jerusalem after Shultz met Monday with Israeli Prime Minister Yitzhak Shamir, Foreign Minister Shimon Peres and Defense Minister Yitzhak Rabin.

A senior Israeli defense official said, meanwhile, that the government remained deadlocked and the only way to gain acceptance of the plan would be for Shultz to persuade Hussein to accept it.

"I feel it can bring about a change," the Israeli official said in a briefing for American reporters, under rules that barred identifying him.

But the U.S. official, who also spoke on condition of anonymity, said Hussein might reply that Israel should act first. The divided Israelis "should pull themselves together as a government," he said.

The U.S. plan calls for three years of self-rule, but not statehood, for the 1.5 million Palestinians living in the occupied West Bank and Gaza Strip. Negotiations on an overall settlement would open in December.

Although Shultz set a mid-March deadline for a reply, Israel, Jordan and Syria all have neither accepted nor rejected the U.S. plan.

With the deadline past, the U.S. official said there was still time for Shultz "to get real momentum" toward a Middle East settlement in the Reagan administration's remaining nine months.