The Obama administration decided to back efforts to create an international commission investigating alleged human-rights violations in Myanmar in a move that ratchets up pressure on the country as it prepares for its first election in 20 years.

The move comes just months after Washington said it was embarking on a new policy of “engagement” with Myanmar aimed at improving relations after years of economic sanctions failed to weaken its secretive military regime. Supporters of the engagement effort, including some Myanmar exiles and analysts, had hoped it would encourage top Myanmar generals to open more to the outside world and take steps to ensure the coming election is held to international standards.

More recently, however, U.S. officials began to express frustration that their overtures—which included visits to Myanmar by high-ranking State Department officials—had failed to influence the government, which is accused of human-rights violations including the imprisonment of 2,000 or more political opponents.

Myanmar’s government has declined to release Nobel laureate opposition leader Aung San Suu Kyi from house arrest, which U.S. officials have said is a precondition to holding fair elections. In June, Myanmar officials issued tough new campaign rules that prohibit political parties from marching or chanting slogans or giving talks “tarnishing the image of the state.” Opposition leaders say they have been harassed by police in recent weeks.

U.S. officials have expressed concern over unconfirmed reports that Myanmar may be attempting to develop a nuclear-weapons program. Those concerns grew more serious in recent months after exile news services released reports about the alleged program based in part on details from a Myanmar army defector. Myanmar officials have repeatedly denied any attempts to develop nuclear weapons.

“The United States supports establishing an international commission of inquiry to investigate alleged war crimes and crimes against humanity” in Myanmar, an administration official said Wednesday. “We have begun consulting with others to determine how best to achieve that end,” the official said.

It wasn’t possible to reach anyone within the Myanmar government to comment.

Critics of Myanmar have been pushing for a United Nations-led inquiry for years. The effort gained momentum this year after a U.N. special rapporteur for Myanmar, Tomas Ojea Quintana, said he found a pattern of systematic human-rights violations in trips to the country, including cases of forced labor.

A Myanmar diplomat disputed the assessment at the time and said international authorities should be more focused on rebuilding relations with the country.

U.S. support doesn’t mean an inquiry will occur. But it indicates that Western governments are hoping to tighten pressure on Myanmar’s military, which has ruled the country since 1962, and especially its top leader, Senior Gen. Than Shwe. Many exiles and academics believe Myanmar’s generals opted to schedule an election this year in part to boost their legitimacy in the international community, potentially forestalling any bid to open a crimes-against-humanity probe.

Myanmar’s officials promise that the vote, scheduled for Nov. 7, will be free and fair. But many opposition leaders, including Ms. Suu Kyi, have vowed to boycott, and international rights groups have said they don’t believe a fair vote can be held given Myanmar’s tight restrictions on the media and public assembly. Opposition leaders easily won the last vote, in 1990, but the junta ignored the results.

The decision to back a commission of inquiry “is the right and timely action by the Obama administration” to express displeasure over what is likely to be a “sham election,” said Aung Din, executive director of the U.S. Campaign for Burma, a Washington group that uses a former name for the country, in a statement.