UPDATE 1-Obama says will not rest until Gulf oil spill plugged

(Adds quotes)

FREMONT, Calif. May 26 (Reuters) - U.S. President Barack Obama said on Wednesday a top-kill procedure being attempted by BP Plc (BP.L) should greatly reduce or eliminate the flow of crude from the Gulf of Mexico oil spill -- if it works.

Obama told a California audience that the "heartbreaking" oil spill underscores the need to find alternative energy sources.

Obama and others in his administration are carefully monitoring BP's latest attempt to stem or stop the flow of oil from the mile-deep gusher.

"If it's successful, and there's no guaranteee, it should greatly reduce or eliminate the flow of oil now streaming into the Gulf from the sea floor," Obama said.

Under pressure to get the leak stopped, Obama said: "We will not rest until this well is shut, the environment is repaired and the cleanup is complete."

(Reporting by Jeff Mason, editing by Jackie Frank)