But the head of the striking Professional Association of Foreign Service Officers said the union is prepared to extend the strike into the fall if necessary.
Clement and Tim Edwards, the union president, both dug in their heels in separate interviews Tuesday after engaging in a heated exchange on Twitter.
The tough talk on both sides does not bode well for the resolution of an unprecedented job action that has reportedly stalled visa processing in Canadian foreign embassies.
That has tourism groups estimating that the strike could cost the industry $280 million this summer, while some foreign students have been forced to withdraw from Canadian university courses because they can't get visas in time.
"I would certainly hope that the union would recommend to its membership that this is an offer worth taking, that it's not going to get any better than this," Clement said in his interview.
"It's better to resolve this and everybody get back to work."
Edwards said that's not likely to happen any time soon under the current circumstances.
"The offer that is on the table, regardless of whether you think it's fair or reasonable, is the same one that's been on the table since we began negotiations 21 months ago, without a single change."
Edwards said the strike is starting to undermine the Canadian economy in tourism, education and agriculture among other sectors, and that his striking membership takes no joy in the dispute.
"We already made preparations to take this through the summer and into the fall."
The union continues to target cabinet level travel abroad, international priorities and visa processing, he added.
Edwards said he was happy to have engaged Clement over Twitter because it shows the minister is paying attention to their situation.
But Clement, who has used Twitter to blast opponents in the past, made clear that he is not going to cede social media space to the union.
"They're trying to pressure me, by social media, to take a position that is contrary to the interests of taxpayers. I guess what I wanted to indicate without any equivocation was that that will not work with me," the minister said from his riding in Ontario's Muskoka region.
"I will not fold like a $3 suitcase."
The union's 1,350 members have been in a legal strike position since April, and have stepped up job action at their Ottawa headquarters and about a dozen foreign missions, including Washington and Hong Kong.
The union wants wage parity with their counterparts in other federal departments that make as much as $14,000 more for doing similar work.
Talks between the two sides broke down earlier this spring when Treasury Board returned to the table with no new offer.
Clement also reiterated another key position of the government: "These are very well paying jobs, highly sought after, in the public service."
NDP foreign affairs critic Paul Dewar, whose downtown Ottawa riding is home to many public servants, urged Clement to get back to the bargaining table with something meaningful for the union.
He accused the minister of being "juvenile" on social media instead of being responsible and seeking a negotiated solution to the standoff.
Clement's remarks on Twitter "were derogatory to the public service," Dewar said.
Clement, however, was adamant he would not cede ground in cyberspace.
"I know sometimes unions try to pressure the bargainer, in this case me, through social media and through a series of advocacies. That will not work with me," Clement said.
"My position is: if you want to do something that's positive and useful, stop being on strike, get back to work and accept a fair and reasonable offer."
Edwards, however, said the government is not bargaining in good faith.
He said the union's wage demand for equal pay would cost the government $4.2 million over three years — a relatively small sum compared with the growing impact of the strike on the Canadian economy.
He said the union would continue to target cabinet level travel abroad, international priorities and visa processing.
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