The Canada Revenue Agency will not extend this year's tax deadline amid a federal public service strike that has seen 39,000 of its workers walk off the job.

The CRA staff are among 159,000 Public Service Alliance of Canada members who went on strike on April 19 over issues including wages and work flexibility. Critics say with CRA phone lines closed or wait times stretching into hours, it will be harder for Canadians to file personal income tax returns by the May 1 deadline.

"I think they're ignoring the fact that the CRA gets hundreds of thousands of calls per week this time of year," Ottawa-based accountant Eric Saumure told CTV News. "This is game time for them, and there's no one there to answer Canadians' calls."

The CRA says that although its phone lines are closed or operating at "reduced agent capacity," the filing deadline has not changed and that overdue taxes are subject to penalties and interest.

"However, if circumstances beyond the control of a Canadian or business prevent them from meeting their tax obligations, the CRA may provide relief from penalties or interest," a CRA spokesperson said in a statement to CTV News. "Canadians must first apply and each file is assessed on a case-by-case basis."

Information on applying for relief can be found on the CRA website.

Saumure has launched an online petition urging the CRA to extend the personal tax filing deadline from May 1 to June 15. So far, it has received over 26,000 signatures.

"I wrote it because I saw that there was over a three-hour wait on the CRA phone lines, and I knew that just wasn't acceptable to most Canadians," Saumure said. "Most Canadians don't have access to knowledgeable accountants and they need to call the CRA, and if they have to wait on the phones for three to four hours, that is not OK."

Minister of National Revenue Diane Lebouthillier maintained the government's stance during question period on Tuesday.

"The Canada Revenue Agency will not change the tax filing deadline because the work stoppage does not prevent Canadians from submitting or filing online or on paper by the deadline," Lebouthillier told parliament in French.

Saumure believes that's not true.

"There has been an incredible impact on low income Canadians and on seniors around the country," he said. "It's similar to if you're having an exam, and you just can't ask questions to your professor. And if you get the answer wrong, there's a penalty, there's a financial penalty, and people can't afford these penalties right now."

With files from The Canadian Press