US President Barack Obama arrived back in chilly Washington on Sunday after a 16-day holiday in his native Hawaii, but his wife Michelle was not with him.

Obama swapped the sun-dappled golf courses of tropical Hawaii for a Washington in the grip of an Arctic cold snap this weekend, and faces a tough political season ahead.

The US president left Honolulu's Joint Base Pearl Harbor-Hickam on Air Force One just before 9:00 pm on Saturday (0700 GMT Sunday) with his daughters, before arriving in the US capital eight hours later.

"As part of her birthday gift from the president, the First Lady will remain in Hawaii to spend time with friends ahead of her upcoming 50th birthday," a brief White House statement said. Michelle Obama's birthday is on January 17.

Obama arrived in Hawaii on December 21 along with Michelle and daughters Sasha, 12, and Malia, 15, and enjoyed several rounds of golf during his stay including with New Zealand Prime Minister John Key, a rare vacation encounter with a foreign dignitary.

The Obamas stayed at a rented house near a US Marine Corps base on the northeastern coast of the island of Oahu, located about a dozen miles (20 kilometers) from the state capital Honolulu, where Obama was born.

Obama's approval rating is languishing at near record lows and he is locked in a Cold War with a surly Congress. He needs quick victories in the run-up to his State of the Union address at the end of the month, observers say.