Secretary of State George P. Shultz today made a personal appeal for approval of his embattled choice to be assistant secretary of state for European affairs, Richard R. Burt.

Burt, 35, has been the target of a small group of conservative Republican senators led by Orrin G. Hatch (R-Utah) and Jesse Helms (R-N.C.) who question Burt's position on a variety of arms control issues, sanctions on trade with the Soviet Union and limitations on arms sales to Taiwan.

Burt's nomination to the top European post in the State Department was sent to the Senate Foreign Relations Committee by President Reagan in August and was approved in September after hearings. But the conservatives, part of an unofficial group known as the steering committee, have prevented a final confirmation vote by the full Senate and thus continue to block Burt's official appointment.

Today, Shultz told reporters, and presumably Congress, "I want to pay a compliment to the European bureau and particularly to Rick Burt, who has done a very good job in the preparations and the work" during Shultz's 13-day European swing, now about half over.

Shultz said that "every indication I have at the White House, from the president, is that he is the president's nominee and we are supporting him."

Although Republican Senate leader Howard Baker has indicated that the Burt confirmation vote may be delayed until the next session, Shultz said he told Baker before leaving that the issue was important to the department and "I don't count it out this session."

Burt also is accused by his opponents of reporting classified information that was leaked to him when he was a New York Times reporter. Shultz said whoever leaked the material is at fault and that Burt "worries a lot about security."