Senate challengers of Richard R. Burt's confirmation as assistant secretary of state for European affairs, suspecting that he has undercut tough negotiations with communist countries, are demanding the records of policy positions taken by the State Department in meetings with the National Security Council and other agencies.

The Burt nomination is one of several disputed nominations scheduled to be called up today on the Senate floor amid threats of a filibuster.

In preparation for a possible showdown today, Sen. Orrin G. Hatch (R-Utah), speaking for himself and "my colleagues" among conservative Republicans, submitted a 13-point broadside of accusations against Burt. They question his positions on nuclear arms control policy, sanctions on trade with the Soviet Union in the pipeline dispute and limitations on arms sales to Taiwan, among others.

Hatch said yesterday that he wrote two letters to Burt last Friday following a meeting of the Senate Steering Committee, an unofficial group of Republicans, with Burt and Powell Moore, assistant secretary of state for congressional relations.

In one letter, Hatch said "long-term suppporters of President Reagan like ourselves have been appalled at these reports of the positions you have taken." Hatch said the only way "to satisfactorily refute" the accusations "would be to provide us with copies of the State Department positions submitted to NSC or inter-agency meetings about these issues."

It is standard practice in the executive branch to deny requests for records of inter-agency policy debates on grounds of executive privilege, and the State Department yesterday declined to comment on any of the issues raised in Hatch's letters.

Hatch was in a Salt Lake City hospital yesterday recuperating from surgery, but said he expects to be in the Senate today and awaits responses. According to Hatch, Burt answered "three or four" questions Friday, denied those accusations, and said he is prepared "to answer all questions." Burt is traveling with Secretary of State George P. Shultz in Europe.

Among the matters that Hatch said await answers are charges that Burt, inside the administration, originally opposed "the zero option" in negotiations with the Soviet Union on limiting European-based nuclear weapons, "opposed raising any Soviet violations" of agreements on limiting intercontinental nuclear missiles, and opposed continuing sanctions on allied nations helping to equip the Soviet natural gas pipeline.

Burt also was questioned by Hatch about meetings with New York Times reporter Judith Miller and her "articles on arms control appearing so soon after your own meetings with her." Other sources have said that Burt, who has declined public comment on the accusations, denied leaking any stories to Miller and denied the other charges by the Senate critics.