Teodoro Locsin Jr, or "Teddy", tweeted seemingly pro-Nazi comments, with references to Auschwitz and the "Final Solution".
Mr Locsin later apologised for the tweets and removed several of them.
The 67-year-old is a journalist and ex-congressman.
His tweets echo recent comments made by Philippine President Rodrigo Duterte, who prompted outrage by referring to the Holocaust and saying he would be "happy to slaughter" three million drug addicts.
More than 3,000 people with alleged links to drug use or dealing have been killed since Mr Duterte came to power in June.
Mr Locsin started gaining attention on the social platform after he posted several controversial tweets.
"I believe that the Drug Menace is so big it needs a FINAL SOLUTION like the Nazis adopted. That I believe. NO REHAB," he tweeted on the 21 August.
In another tweet he referenced Auschwitz, the concentration camp run by the Nazis in which almost a million Jews were killed.
The petition, addressed to the UN, called for Mr Locsin's appointment to be denied, saying that "his blatant justification of anti Semitic lingo makes him a racist, clearly showing his prejudice against the Jewish people".
Reaction to Mr Locsin was swift, with some on Twitter calling him a disgrace.
"You're making this country look crazy," a user commented.
"I thought ambassadors are supposed to be educated. I guess the UN just skipped that process when appointing Teddy Locsin." another said.
"You're a disgraceful UN ambassador to the country," one added.
However, Mr Locsin also had his share of supporters, with one saying that "lots of us want you at the UN just the way you are - sarcasm and all".
Mr Locsin, who served as a local politician for almost 10 years, has accepted the post of Philippines permanent representative to the UN but is awaiting official governmental confirmation.
Amid reaction to his comments, Mr Locsin said that his daughters had told him to "stay out of Twitter", adding that he was not allowed to tweet anything, "not even niceties".
He also apologised for his tweets.
"I am sorry for my strong language, but it is unavoidable given the mendacity of those I fight. I cannot be other than myself," Mr Locsin tweeted on Friday. " I ask God's and the Jewish community's forgiveness, but only theirs."
Mr Locsin also told CNN that his tweets had been sent for "shock value", and was "partly a private joke" between him and a friend who worked in the Jewish government district.
The office of the Philippine delegation to the UN declined to comment on the matter.

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Match referee Evan Boyce took no action at the time but notified the IFA's Disciplinary Committee regarding the incident following the Solitude game.
It considered the correspondence together with video footage.
Oman was charged with a breach of Article 18.11 of the Disciplinary Code (assault or battery of an opponent).
Portadown were also fined £100 by the Disciplinary Committee.
Cliftonville won 1-0 in what was Niall Currie's first game in charge as Portadown manager.
A petition to reject the controversial nominee for Philippine ambassador to the UN has reached more than 10,000 signatures, after he was seen using anti-Semitic language on Twitter.
[NEXT_CONCEPT]
Portadown defender Ken Oman has been suspended for six matches for elbowing Cliftonville's Caoimhin Bonner in Saturday's Premiership fixture.