SEOUL (Reuters) - Former New Mexico Governor Bill Richardson and Google Executive Chairman Eric Schmidt began a controversial private mission to North Korea on Monday that will include an effort to secure the release of an imprisoned American.

The trip comes after North Korea carried out a long-range rocket test last month and as, according to satellite imagery, the reclusive state continues work on its nuclear testing facilities, potentially paving the way for a third nuclear bomb test.

Footage from North Korean state television showed Richardson and Schmidt at the Pyongyang airport on Monday evening.

“We are going to ask about the American who’s been detained. A humanitarian private visit.” Richardson said.

Richardson’s efforts to seek the release of Kenneth Bae, a Korean-American tour guide who was detained last year will mark the latest in a series of high-profile visits over the years to free Americans detained by Pyongyang.

The delegation comprised Schmidt, his daughter, Richardson and Google executive Jared Cohen, according to South Korean news media and it arrived in Pyongyang on a flight from the Chinese capital, Beijing.

The mission has been criticized by the United States due to the sensitivity of the timing. The United States does not have diplomatic relations with North Korea and the isolated and impoverished state remains technically at war with U.S. ally South Korea.

“We continue to think the trip is ill-advised,” U.S. State Department spokeswoman Victoria Nuland said in Washington. Last week she said the main U.S. objection was that the trip came so soon after North Korea’s much-criticized December 12 rocket launch.

South Korea is in the midst of a transition to a new president who will take office in February, while Japan, another major U.S. ally in the region, has a new prime minister.

Former New Mexico Governor Bill Richardson (R) and Google Executive Chairman Eric Schmidt (L) arrive at an airport in Pyongyang, in this photo taken by Kyodo January 7, 2013. REUTERS/Kyodo

A U.S. official said the trip’s timing was particularly bad from the Obama administration’s point of view because it comes as the U.N. Security Council ponders how to respond to the North Korean missile launch.

“We are in kind of a classical provocation period with North Korea. Usually, their missile launches are followed by nuclear tests,” said the official, who spoke on condition of anonymity.

“During these periods, it’s very important that the international community come together, certainly at the level of the U.N. Security Council, to demonstrate to North Korea that they pay a price for not living up to their obligations.”

Richardson, a former ambassador to the United Nations, has made numerous trips to North Korea in the past that have included efforts to free detained Americans. The reasons for Schmidt’s involvement in the trip are not clear, though Google characterized it as “personal” travel.

Schmidt did not respond to requests for comment.

Richardson told CBS television last Friday that he had been contacted by Bae’s family and that he would raise the issue while in North Korea.

Pyongyang’s most notable success was securing a visit from former President Bill Clinton in 2009 to win the release of two American journalists.

Last year, Jared and Schmidt met defectors from North Korea, a state that ranks bottom in an annual survey of Internet and press freedom by Reporters Without Borders.

Media reports and think tanks say that officials from the North Korean government went to Google’s headquarters in 2011, something the U.S. technology giant declined to comment on.