* Obama cuts short India trip for 4-hour Saudi stop
* Accompanied by Republican foreign policy veterans
* Likely to discuss Syria, IS, Iran and oil - expert (Adds background about James Baker and other U.S.-Saudi foreign policy issues)
By Roberta Rampton
NEW DELHI, Jan 27 (Reuters) - President Barack Obama will fly a 30-member delegation, including top officials and respected Republican foreign policy veterans, to Riyadh on Tuesday to meet Saudi Arabia's new King Salman as the crisis in neighboring Yemen continues to boil.
The hastily scheduled trip to pay respects following the death last week of King Abdullah underscores a strengthening U.S.-Saudi alliance that extends beyond oil interests to regional security.
Cutting short a three-day trip to India, ID:nL4N0V51WQ Obama's visit comes as Washington struggles with worsening strife in the Middle East and counts Saudi Arabia among its few steady partners in a campaign against Islamic State militants who have seized swathes of Iraq and Syria.
Obama is slated to arrive in Riyadh at 3:25 p.m local time (1225 GMT), and will leave around four hours later.
Following Abdullah's death last Friday, Obama will try to get relations off to a smooth start with Salman, who takes power after a period of sometimes tense relations between Washington and Riyadh.
Obama will bring with him Republican elder statesmen James Baker, secretary of state in the George H.W. Bush administration, Republican Senator John McCain who leads the Senate Armed Services committee, and several other Republican foreign policy leaders from past administrations.
Baker is revered among Gulf Arabs, particularly in Saudi Arabia and Kuwait, for his role in orchestrating the alliance against Saddam Hussein in 1990-91.
YEMEN HEADACHE
The U.S. security headache worsened last week with the take over of Yemen's government by Iran-backed rebels - a setback to U.S. efforts to contain al Qaeda militants there and to limit the regional influence of Shi'ite Iran.
The Yemen government's collapse will be of deep concern to Saudi Arabia because of the long border they share and because of the advance of Iran, Sunni Saudi Arabia's main regional rival.
Saudi Arabia's role in rallying Arab support for action with Western countries against Islamic State militants has won praise in Washington, which with other Western nations also values the kingdom as an important market for defence equipment.
The leaders are likely to discuss Syria, Iran and oil prices, said Simon Henderson, an expert on U.S.-Saudi relations at the Washington Institute for Near East Policy.
"The most interesting question for President Obama will be whether King Salman and his team of advisers have an order of priority that differs from King Abdullah's," Henderson wrote in a comment on Monday.
IMPATIENCE WITH WASHINGTON
Despite an alliance between the two countries that has long been a cornerstone of U.S. Middle East policy, Riyadh has made clear its impatience with the Obama administration's failure to do more to oust Syrian leader Bashar al-Assad and its anxiety over U.S.-led efforts to negotiate a nuclear deal with Iran.
This added to a sense among Saudi rulers that Obama was neglecting old Arab allies, most notably with the U.S. abandonment of Egyptian President Hosni Mubarak when he was toppled by mass protests in early 2011.
Saudi Arabia remains unhappy with Obama's resistance to large-scale U.S. arming of the mainstream Syrian rebels.
The booming domestic energy sector has the United States less reliant on Saudi oil supplies. But the kingdom's willingness to keep oil output high despite tumbling global oil prices has bolstered the U.S. economy and U.S. efforts to pressure oil producers Russia and Iran with economic sanctions.
Still looming, however, is the prospect of a nuclear deal with Iran, which would be major legacy achievement for Obama but which Saudi Arabia worries could help strengthen Tehran's influence in the region.
U.S.-Saudi relations improved after Obama made a fence-mending visit to Riyadh last March.
Obama's Secretary of State John Kerry and CIA Director John Brennan will be part of Tuesday's delegation, as will top Obama advisers Susan Rice and Lisa Monaco.
Other Republicans in the large delegation will include Brent Scowcroft, national security adviser to Presidents Gerald Ford and George H.W. Bush, and Condoleezza Rice, secretary of state for President George W. Bush.
Also included are former national security advisers Sandy Berger of the Clinton administration and Stephen Hadley from the George W. Bush White House.