Baird issued the warning just as the federal government considers whether to end hundreds of millions of dollars in Canadian humanitarian aid to the Palestinians when it expires at the end of this month.
Baird delivered his message to an approving audience Sunday in Washington at the annual conference of the American Israel Public Affairs Committee.
Canada strongly opposed the Palestinians' successful effort in November to win elevated status at the UN, and has warned them against using it to file an international legal complaint against Israel.
It has also opposed the Palestinian bid to win membership with the United Nations cultural organization, UNESCO.
Palestinian officials have said they would have no choice but to pursue Israel at the International Criminal Court to halt construction of new settlements in what it claims as its territory.
The settlement issue wasn't raised in the panel discussion, but Baird was asked by a moderator what "the repercussions might be from your country" towards the Palestinians if they went to the ICC.
"We were very clear from the outset that further actions, like we've seen at UNESCO, like we've seen at the United Nations, particularly at the International Criminal Court will be ones which will not go unnoticed and will have certainly consequences in the conduct of our relations with the Palestinian Authority," Baird replied.
"We hope that they will honour the commitments that they made that they would not do that."
Prime Minister Stephen Harper also issued that warning privately to Palestinian leaders last fall in New York.
An online video of the Baird event shows the minister receiving a boisterous, upbeat welcome from the delegates, a reflection of satisfaction with his and the Harper government's unwavering support of Israel.
Baird's office offered no explanation for why it didn't publicize his appearance there prior to the event, and referred calls about the Palestinian funding to the Canadian International Development Agency.
International Co-operation Minister Julian Fantino was non-committal Tuesday about future funding to the Palestinian Authority beyond this month.
"We are undertaking a normal review of our program with the PA based on outcomes achieved with taxpayer dollars, as we do with all of our programs," the minister said in written remarks.
"Future commitments with the PA will be dependent on our ability to achieve meaningful results with taxpayer dollars and the commitment of the PA to prioritize the basic needs of the people."
The Palestinian delegation in Ottawa had no comment.
Baird offered his audience new perspectives on the vexing Middle East impasse, expressed concern about the stability of Egypt and endorsed Italy's former foreign minister as the next chief of NATO. His passionate defence of the expulsion last year of Iranian diplomats from Canada earned him a standing ovation.
Baird also criticized the speech that Palestinian President Mahmoud Abbas delivered at the UN General Assembly in November following the successful Palestinian bid for statehood.
"He was going in knowing he was going to win and win big," Baird said. "He could have extended an arm, a hand to Israel. He could have extended an olive branch. He could have been generous, and we didn't see any generosity in his remarks.
"And that deeply, deeply concerned many of us."
Baird made a special trip to the UN General Assembly that very day to oppose the Palestinian bid, which in the end won overwhelming support.
Canada, the United States, Israel and six other, smaller countries were the only UN members to vote against the Palestinians in the 193-country general assembly.
Baird earned applause when he fired back at critics who have said Canada isolated itself internationally, saying his government will not "go along to get along with some moral relativist crowd at the United Nations or elsewhere."
"We have seen this in the conduct of international diplomacy — this push to go along to get along. Go along with the pack, go along with the crowd. Well, listen — parents around the world tell their kids that's wrong ... and it's certainly wrong in the halls of the United Nations," he said, sparking a fresh round of applause.
Baird was joined at Sunday's event by the former Italian foreign minister, Franco Frattini, who is in the running to be next secretary general to NATO.
Both politicians offered warm praise for Israel and outspoken condemnation to its critics during their 25-minute appearance.
"Wouldn't he make a great secretary-general of NATO?" Baird quipped after Frattini offered a strong denunciation of anti-Semitism.
Baird also went beyond his usual talking points when he was asked for his views on the aftermath of the Arab Spring in the Middle East and North Africa.
"Until these economies get up and running, until they see some economic growth, until they see substantial job creation, the political instability is going to continue," he said.
Baird said he was concerned about Egypt, which has been gripped with violent protests against the country's new rulers.
"That's something that we've got to stay focused on, particularly if you look at the situation in Egypt," he said.
"If the economy doesn't get going there, if there's not meaningful numbers of jobs created, it's going to be a real problem for the stability of the country, and certainly the stability of the government."
Baird won an extended standing ovation for reiterating the government's view that Iran's pursuit of a nuclear weapon is the most dangerous threat to global security.
He delivered that message with a soaring rhetorical flourish, and sparked laughter when he deadpanned: "I was warned this would be a tough crowd."
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