A bill authorizing $2.9 billion for health manpower programs over the next four years cleared the House by voice vote yesterday after sponsors cut the total to ease Republican and Reagan administration opposition.

Rep. Henry A. Waxman (D-Calif.), sponsor and floor manager of the measure, which provides authorizations for the National Health Service Corps, community health centers, migrant health programs and doctor and other health professional training, said, "We're hopeful the administration will endorse it" now that the funding has been reduced.

As reported out by the Energy and Commerce Committee, the bill authorized $3.1 billion over the four years. Before yesterday's cutback, an administration spokesman said: "We are against the . . . bill because it costs too much money. We favored $2.9 billion and they provided $3.18 billion."

Waxman offered an amendment, which he had worked out with leading Republicans, to reduce the total to $2.965 billion and won the support of Rep. Edward R. Madigan (Ill.), the senior Republican on the health subcommittee, which Waxman heads.

An amendment by Rep. William E. Dannemeyer (R-Calif.) to delete an additional $83 million was defeated, 236 to 78.

Before final passage, the House adopted an amendment by Rep. Gerald B. Solomon (R-N.Y.) to bar aid funds to students who are required to register for the draft but who have not done so.

An important feature of the bill is that it provides funds for community health centers as such and not as part of a block grant, which the administration favored.