(Adds White House comment, paragraphs 6-7)

BANGKOK, June 4 (Reuters) - U.S. warships will soon leave waters near Myanmar after the ruling military junta refused permission for the delivery of aid supplies to the cyclone-stricken Irrawaddy delta, a top U.S. commander said on Wednesday.

Adm. Timothy Keating said the USS Essex group will sail away from the former Burma on Thursday but leave several heavy-lift helicopters in neighboring Thailand to help in the relief effort.

"Should the Burmese rulers have a change of heart and request our full assistance for their suffering we are prepared to help," Keating, commander of U.S. forces in the Pacific, said in a statement.

Myanmar has been promised millions of dollars in aid from the United States, other governments and aid organizations. Cyclone Nargis, which hit a month ago, is believed to have left 134,000 people dead or missing and 2.4 million destitute.

But the junta has refused to allow the U.S. military to help distribute aid to affected areas, apparently fearing that a large-scale international relief effort would loosen the grip the generals have held since a 1962 coup.

In Washington, White House spokeswoman Dana Perino again pressed the Myanmar government to allow in aid workers.

"The Burmese regime must permit all international aid workers the access necessary to provide the urgently-needed assistance," she said in a statement. "There is no more time to waste."

Thai Prime Minister Samak Sundaravej told visiting U.S. Defense Secretary Robert Gates in Bangkok on Sunday that the junta had rejected foreign military help in delivering cyclone aid because it feared it could be seen as an invasion.

Keating said they had made 15 attempts over the past three weeks to convince the regime to allow in U.S. helicopters and landing craft, "but they have refused us each and every time."

The United States had delivered more than 2 million pounds of relief supplies on 106 airlifts to Myanmar since the first U.S. military aid flight on May 12, Keating said. (Reporting by Darren Schuettler in Bangkok, Jeremy Pelofsky in Washington; Editing by Doina Chiacu)

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