Rep. Jack Kemp (R-N.Y.), in another skirmish with political rival Vice President Bush, has sharply criticized the Reagan administration's decision to nominate a prominent Bush supporter to head the United Nations Development Program.

In a letter to Secretary of State George P. Shultz, Kemp attacked the nomination of William H. Draper III, most recently president of the Export-Import Bank, to head the U.N. agency. Kemp and three other conservative House Republicans complained in a Feb. 21 letter that Draper approved export loans to Angola -- where the administration is now supporting rebels against the Marxist regime -- and that Draper's views on abortion are at odds with Reagan's.

Kemp, joined by Rep. Henry J. Hyde (R-Ill.), Rep. Vin Weber (R-Minn.) and Rep. Christopher H. Smith (R-N.J.), said "there will be very serious consequences for the president's foreign aid package in Congress" if Draper is appointed. However, two other congressmen, Gerald B. Solomon (R-N.Y.) and Gus Yatron (D-Pa.), have expressed support for Draper.

The Kemp letter is not likely to impede Draper's nomination, which has been proposed by the United States and must be approved by the U.N. General Assembly, but it does reflect the intensifying contest between Bush and Kemp for the 1988 GOP presidential nomination.

Draper, who was reportedly backed by Bush for the U.N. post, said yesterday he has "no differences with the president's policies overall." The loans to Angola in 1984 could not be refused to the companies that applied under the existing law, he said. He also denied that he had opposed Reagan's position at the Mexico City conference on population policy, but said he did differ with delegation head James Buckley on abortion and family-planning issues.

Draper said he is a "very strong Bush advocate" and worked on his recent campaigns.