Begich, an Alaska Democrat, was one of four Democratic senators invited by the White House to meet with Obama to discuss the federal budget and other issues.
The meeting was closed to the press, but Begich, a proponent of the oil and gas industry, said he pressed for increased drilling and missile defense during the 45-minute session with Obama.
The president himself cited the importance of Alaska's natural gas pipeline and listened to his concerns, Begich said.
Obama's budget proposal would eliminate several tax incentives and increase taxes on the oil and gas industry, Begich said. By some estimates, the budget could cost the industry as much as $31 billion, Begich said - money the administration wants to use to fund development of renewable and alternative energy sources.
While he supports new energy sources, Begich said fossil fuels will continue to heat American homes and fuel its vehicles and factories for years to come. He said he urged Obama to work with Congress on a comprehensive energy policy that incorporates important Alaska energy resources, such as an Alaska natural gas pipeline and new oil reserves in the Arctic.
On missile defense, Begich said he urged Obama to continue the ground-based missile defense system being built at Fort Greely, 100 miles southeast of Fairbanks. The system is designed to protect against missile attacks from countries such as North Korea, which is reportedly testing missiles capable of reaching Alaska.
Begich, a member of the Senate Armed Services Committee, said any proposal to reduce spending on missile defense must be supported by military-focused justifications. Defense Secretary Robert Gates has said that North Korea and Iran remain "vexing challenges" and have ballistic missile programs of noteworthy range.
Begich said he also stressed the importance of the tourism industry, which brings in an estimated $1 billion a year to Alaska's economy and supports thousands of jobs.
Also attending the meeting were White House budget chief Peter Orszag and Sens. Byron Dorgan of North Dakota, Blanche Lincoln of Arkansas and Jeanne Shaheen of New Hampshire.