China's leaders, renowned for their hospitality, are proving difficult to line up as guests--at least at the White House.

President Reagan sent a personal invitation to Premier Zhao Ziyang last week, suggesting he visit sometime this year, possibly June or September. The message was delivered by Secretary of State George P. Shultz who had come to Peking to inject some personal statesmanship into the sagging bilateral relationship.

Zhao accepted the invitation in principle, as he did the last one presented him 19 months ago, but hedged on a date. He told reporters he hopes that "failure to remove the obstacles" blocking better relations, chiefly the Taiwan issue, will not interfere with his visit.

"Nor do I believe such situations would happen," he added.

When the White House interpreted this to mean he was coming in 1983 and announced the meeting, China's Foreign Ministry promptly responded with a denial.

"Both parties did not decide that Premier Zhao will visit the United States within this year," said a spokesman.

While no one is ruling out a visit, Peking's conspicuous hesitation is seen here as another sign of displeasure over U.S. arms sales to Taiwan. On the day of Shultz's departure, the state-run news agency reported that Chinese leaders had told the secretary that better relations and mutual trust were "out of the question" until the Taiwan question is resolved and the U.S. side lives up to an August communique aimed at settling the controversy.

"They have to show a little distance and disapproval," observed a Western European diplomat. "Zhao just can't be seen running off to Washington at Reagan's beck and call."

No ranking Chinese leader has been to the United States since Deng Xiaoping visited in the 1979 bloom of normalization. China has hosted visits by Vice Presidents Bush and Mondale, former presidents Nixon, Ford and Carter and a steady stream of congressmen, Cabinet chiefs and secretaries of state.

"Why should there be so much fuss over protocol?" asked an influential Chinese journalist, smiling knowingly.

In fact, Peking places a high premium on personal diplomacy. Sino-American relations got off the ground in 1972 when Richard Nixon clinked glasses here with the late premier Chou en-Lai. Deng's U.S. trip is said to have created more good will on both sides than hundreds of communiques.

Zhao, since becoming premier in late 1980, has traveled to dozens of countries. He just returned from an 11-nation African tour, which was touted as evidence of China's new independence from superpower concerns and of commitment to the Third World.

Shultz had hoped his four-day mission would result in a date for Zhao's U.S. visit. Of the two months Reagan proposed in his letter, Zhao rejected June because of an important national legislative meeting falling in that month, said Chinese sources. September seemed like better timing, but the premier refused to commit himself.

Shultz had sought to place the Taiwan matter in the background of his talks. But his hosts stressed that before there can be any improvement in bilateral relations, "it is imperative to remove the obstacles in their way, chiefly the Taiwan question and U.S. arms sales to Taiwan," China's official news agency reported Sunday.

They are reported to have complained of U.S. bad faith in observing the August communique. In it, Washington agreed to phase out weapons sales to Taiwan, with future supplies not to exceed the quantity and quality of arms provided since the establishment of U.S.-Chinese diplomatic relations in 1979.

Chinese leaders reportedly reopened the contentious issue of quantitative limits--specifically, whether they would be set by the number of weapons or dollar value since 1979--a point left vague in the communique.

Shultz emphasized that Washington intends to fulfill its obligations, but he refused to spell out how. "I didn't try to renegotiate that communique with the Chinese, and I don't think I want to do it here either," he told the press before leaving Peking.

Western diplomats believe Zhao may be waiting for a clearer reply before setting foot in the White House. Chinese leaders have shown distrust of Reagan because of his stances on the Taiwan issue and said they have been tricked before.