The Public Service Alliance of Canada says the plane was carrying a French-language banner on Saturday that translates into "Stephen Harper hates us."
An RCMP spokeswoman said in an email that the plane appeared to be flying within restricted airspace over Parliament Hill so the Mounties requested it land.
"The RCMP is mandated with the security on the grounds of Parliament Hill and the RCMP takes all threats seriously," said Cpl. Lucy Shorey.
The RCMP questioned the pilot and determined there was no security threat and considers the matter closed, Shorey said.
Larry Rousseau, regional executive vice-president for PSAC in the national capital region, says the bottom line for the union is that the plane had to land sooner than it had planned.
"The message stopped being apparent to the public," Rousseau said in an interview Monday night.
"Anyway I analyze it, upways, sideways, verticalways, I really have to ask the question, what was the real purpose for asking the plane to come down?” he said.
”What the effect of that (the decision to ask the plane to land) was.....was to get that banner out of the sky."
The plane had been towing the banner over Montreal and other communities in Quebec recently, something the RCMP could have easily checked out, Rousseau said
"Here you have a plane, duly registered, owned by a company that does publicity and that has been flying over many regions of Quebec over the past two weeks."
The Mounties could have had a radio conversation with the pilot to find out what he was doing instead of telling him to land, Rousseau added.
A union news release indicates the pilot was aware of airspace restrictions in place in Ottawa and says Nav-Canada has confirmed the plane did not venture into the restricted zone.
"I have to exclude the national security reasons," said Rousseau.
The union has been waging a public relations battle with the Harper government over its plans to slash thousands of public sector jobs and has received a favourable response from its members over its airborne campaign, Rousseau said.
”We certainly want to see that plane back up on the air as soon as we can.”