Journalists shouted back that the two situations were not comparable because one is a state visit while the other is to a religious body. Le Pen dismissed the criticism.
French law already bans headscarves in all classrooms except universities. She has proposed extending the 2004 law banning headscarves and other "ostentatious" religious symbols in classrooms to all public spaces. While the law covers all religions, it is widely viewed as aimed at Muslims.
When asked if she fears her proposal may ignite the anger of the Muslim community, she said: "When in Rome do as the Romans do."
The headscarf incident occurred ahead of a scheduled meeting with Lebanon's grand mufti, Sheikh Abdel-Latif Derian.
Shortly after Le Pen arrived at his office, one of his aides handed her a white headscarf to put on. Following a discussion with his aides that lasted a few minutes, she refused and returned to her car.
Le Pen said she had informed her host the night before that she would not wear the scarf but they didn't cancel the meeting. Instead, she said, "They tried to impose it upon me."
She said the Grand Sheik of Al-Azhar, the head of the Sunni world's most prestigious learning institute, didn't require her to don the headscarf. Photos of Le Pen with Ahmed al-Tayeb in 2015 in Cairo show her with her hair uncovered.
The officials at the mufti's office "kept the meeting and consequently put me before a fait accompli," she said. "I stuck to my position, because when I take a position it corresponds to a conviction. If (you don't like it) never mind."
The office of Lebanon's mufti issued a statement saying that Le Pen was told in advance through one of her aides that she would have to put on a headscarf during the meeting with the mufti.
"This is the protocol" at the mufti's office, the statement said. It said the mufti's aides tried to give her the headscarf and that Le Pen refused to take it.
"The mufti's office regrets this inappropriate behavior in such meetings," the statement said.
Le Pen has tried to raise her international profile and press her pro-Christian stance with her visit to Lebanon, a former French protectorate.
On Monday, she met with President Michel Aoun, a Christian, and Prime Minister Saad Hariri, a Sunni Muslim. She said Syrian President Bashar Assad was "the most reassuring solution for France," adding that the best way to protect minority Christians is to "eradicate" the Islamic State group.
In her final press conference, she said that there is currently no alternative to the Assad government. She said she considered it a "mistake" that the French government had closed its embassy in Damascus, which undermined relations between French and Syrian security agencies that she said could have helped thwart terrorist attacks in France.
Some Lebanese officials, including Hariri, have taken umbrage at what is widely seen as her stigmatization of Muslims, whom her supporters claim are changing the Christian face of France.
There was also apparent displeasure at her comments on Assad, including from some Lebanese allies.
Christian right-wing leader Samir Geagea said after meeting with Le Pen that "terrorism has no religion." He described Assad as "the biggest terrorist in Syria and the region."
Walid Jumblatt, a leftist politician in Lebanon, tweeted that Le Pen's statements in Lebanon "were an insult toward the Lebanese people and Syrian people."
Later Tuesday, a group of Lebanese held a small protest in Beirut against Le Pen's visit. One protester raised a drawing of Le Pen between Russian President Vladimir Putin and U.S. President Donald Trump, with "Neo-fascists" emblazoned underneath.
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Associated Press writers Sarah El Deeb in Beirut and Elaine Ganley in Paris contributed to this report.
