Lee's administration proposed legislation this month to recognise some rights for same-sex partners whose marriages are registered abroad.
Despite LGBTQ activists arguing it does not go far enough, the proposal drew near-universal criticism from the pro-Beijing politicians that dominate Hong Kong's legislature.
The clash pitted Lee against conservative lawmakers from his own camp and led some to fear the proposal might be pulled.
The city's top court ordered Hong Kong's government to create an "alternative framework" for LGBTQ couples when it quashed a bid to recognise same-sex marriage in 2023.
Lee said on Tuesday the government "must not act in violation" of the Court of Final Appeal's judgement.
"Otherwise, it will be against the rule of law... Violating the rule of law will mean serious consequences," he told reporters.
The government will respect the legislature's final decision, he added.
In 2023, the court unanimously defined marriage as "confined to opposite-sex couples" -- a stance Lee reiterated on Tuesday.
LGBTQ activists say the bill -- which only covers "rights related to medical matters" and "right to handle after-death arrangements" -- fails to satisfy the court's framework requirements.
China is not among the countries around the world that have legalised marriage equality since the Netherlands became the first to do so in 2001.
Hong Kong is a special administrative region of China with its own legislature and a mini-constitution that guarantees a "high degree of autonomy".
Pro-Beijing firebrand lawmaker Junius Ho earlier floated the idea of asking Beijing's top legislature to overrule Hong Kong's apex court to "protect traditional family values".
Support for same-sex marriage in Hong Kong has grown over the past decade and hit 60 percent, according to a 2023 survey.
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