WASHINGTON — Singapore’s foreign minister has pledged that his country will investigate the death of an American engineer whose family rejects a Singaporean police finding that their son committed suicide.

The death of the American, Shane Todd, whose body was found in his Singapore apartment hours after his last day of work for a government research agency there, has threatened to undermine the cordial relations between the United States and Singapore.

Singapore’s foreign minister, K. Shanmugam, met in Washington on Tuesday with Senator Max Baucus, who has been pushing for American involvement in the inquiry, and on Wednesday with Secretary of State John Kerry and Attorney General Eric H. Holder Jr.

Mr. Shanmugam pledged a full investigation and welcomed the involvement of Mr. Todd’s family. “There will be a public inquiry where all the relevant evidence will be presented,” he said, adding that Mr. Todd’s family will be entitled to appoint their own lawyers and take part in the investigation.