The CSeries planes are made at the firm's plant in Belfast, Northern Ireland.
May has been warned if Bombardier is ruled against in the USA - and the country refuses to order the planes - its operation in Ireland could be killed off risking all 4,500 jobs at the company's airplane-wing production factory in Belfast.
American aircraft manufacturer Boeing has accused rival Bombardier of receiving unfair state support and a ruling in the USA this month could doom its Belfast factory.
THERESA May asked Donald Trump to intervene in a trade dispute that threatens thousands of Northern Irish jobs after being pressured by the Democratic Unionist Party, it was claimed last night.
According to the Times, May raised the issue with Trump on Tuesday in a telephone call between London and Washington.
The US-based International Trade Commission will make an initial ruling on September 25 when industry figures expect it to order a punitive tariff of $30 million per aircraft.
The British government said in a statement that Britain's priority is to encourage Boeing to drop the case in favor of a negotiated settlement.
It followed a visit from Greg Clark, the business secretary, to Chicago last month to meet Boeing's chairman and chief executive and plead with them to drop the case.
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In 2016, Canadian firm Bombardier won an order to supply up to 125 CSeries passenger jets to U.S. airline Delta.
"It is in everyone's interests that we safeguard Bombardier's operations and the highly skilled workers that it has in Belfast".
Asked by a lawmaker in parliament whether the government would stand firmly behind Bombardier, Claire Perry, Minister for Climate Change and Industry, said: "It is vitally important that we have this dispute settled and we create the environment for many manufacturing companies in this vital sector to thrive and grow".
A spokesman for May said Bombardier's jobs were "of huge importance" to Northern Ireland.
"The engagement at governmental level with Boeing and with the USA has been significant over the course of the summer because this is pivotal to the Northern Ireland economy", DUP lawmaker Gavin Robinson told the Irish national broadcaster RTE.
Tariffs could make it very hard for Bombardier to find new CSeries customers in the US.
Mrs May's call to the United States president was described as constructive by officials at the Department for Business, Energy and Industrial Strategy (BEIS).
Bombardier condemned Boeing's position as "an unfounded assault on airlines, the travelling public and further innovation in aerospace".
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