Bombardier is Northern Ireland's largest manufacturing employer and May's Conservatives are dependent on the support of the small Northern Irish Democratic Unionist Party (DUP) for their majority in parliament.
Boeing has filed a petition with the US International Trade Commission and the US Department of Commerce alleging that Bombardier is unfairly subsidized by the Canadian and Quebec governments, a claim that Bombardier fiercely denies.
The Prime Minister raised a court case involving US-based Boeing and Canada's Bombardier during a call to the President last week.
A USA ruling against Bombardier this month over punitive tariffs for the aircrafts would be devastating news for the Belfast plant, where some 4,500 people are employed.
The State Department says selling the Super Hornets to Canada would contribute to the US government's foreign policy and national security objectives.
Of the company's nearly 8,000 Northern Ireland employees, about 4,200 work exclusively on aeronautics.
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The leaders of Britain and Canada are set for talks next week on a crisis between Boeing Co and its Canadian rival Bombardier that could have major political implications for both countries, a source close to the matter said on Tuesday.
As the wings for the jets are built at Bombardier's Belfast plant, this could threaten jobs in Northern Ireland.
'We will continue our efforts to secure a resolution'.
"It is in everyone's interests that we safeguard Bombardier's operations and the highly skilled workers that it has in Belfast".
In a statement, Boeing said the company "had to take action as subsidised competition has hurt us now and will continue to hurt us for years to come ..." "We believe that global trade only works if everyone plays by the same rules of the road, and that's a principle that ultimately creates the greatest value for Canada, the United Kingdom, the United States and our aerospace industry".
Mrs May's call to the U.S. president was described as constructive by officials at the Department for Business, Energy and Industrial Strategy (BEIS).
Bombardier has criticized Boeing's complaint, calling it an "unfounded assault" on airlines. It has also complained about a £113 million loan ($150 million) from the British government.