* Saudis to start pulling out from Monday - Bahrain source

* State of emergency was lifted on June 1

RIYADH - Saudi Arabia will withdraw most of its security forces from neighbouring Bahrain, where they helped quell protests in March, a Bahrain government source said on Tuesday.

Security forces from Saudi Arabia and the United Arab Emirates were sent into Bahrain in mid-March to help clear the streets of protesters who had been staging demonstrations since February. Emergency rule, imposed at the time, was lifted earlier this month.

"The Saudi troops will be withdrawn starting on Monday because their situation is getting much calmer," the source said.

Another source confirmed the withdrawal and said not all the troops would leave at once. About 1,000 Saudi soldiers entered Bahrain to protect government facilities.

The Sunni rulers of Bahrain had faced weeks of protests led mostly by the country's Shi'ite majority, and accused demonstrators of pushing a sectarian agenda with the backing of Shi'ite power Iran. The opposition denied this and said it was seeking greater political freedoms and access to jobs.

Bahrain, where the US Fifth Fleet is also based, said it had asked for support in line with a defence pact between Gulf Cooperation Council countries, which include Bahrain, Kuwait, Oman, Qatar, Saudi Arabia and the United Arab Emirates.

"The draw down of Saudi troops from Bahrain signals that the Bahraini forces and police can now secure the situation on their own," said Theodore Karasik, director of research and development at Middle East think tank INEGMA, adding that Bahrain had managed to beef up its forces over the past couple of months.