French President Emmanuel Macron put the item on the agenda of the two-day Summit for a New Global Financing Pact which brought together around 40 heads of state and government.
The shipping industry transports around 90 percent of traded goods worldwide and accounts for around three percent of global carbon emissions.
The Marshall Islands and Solomon Islands have been pushing for a $100-per-tonne tax on emissions which would raise approximately $60-80 billion (55-73 billion euros) of tax receipts per year, according to the World Bank.
At a closing press conference, Macron said that backing from China, the United States and other European nations was still needed in order to bring the idea to fruition.
"We are in favour of taxing shipping, it's a sector that isn't taxed," he told reporters. "To make it work, you need a group of countries that follow us.
"If China, the United States and other key European countries which host major companies, if they don't follow then it won't have any effect."
He cited France's decision to put in place so-called "green taxes" on airline tickets and some financial transactions in the past, saying other countries had not followed suit, putting the country at a disadvantage.
"We can't continue to do harm to ourselves on our own," he said.
US Treasury Secretary Janet Yellen told the same press conference that "it's something that the US will look at".
"We are very focused on the need to raise substantial additional resources to address climate change, poverty reduction and other global challenges," she added.
A Treasury official had previously described the proposal as "in its very early days."
The International Maritime Organization (IMO), a United Nations agency, is set to host a summit in two weeks' time where the carbon tax is expected to be discussed.
German Chancellor Olaf Scholz also lent only lukewarm support to the idea, which has been pushed by two Pacific nations, the Marshall Islands and Solomon Islands, over the last decade.
"It's an interesting proposal but we need to work on it more," he told reporters. "There are some countries that are worried because they can only be reached by boat."
Even if a shipping tax is approved, there remain disagreements over how the money raised would be spent.
The industry would like it to be re-invested in technology to reduce shipping emissions, while the original backers of the idea want the funds used to finance climate change adaptation efforts in poor countries.
A total of 18 countries are currently in favour of the idea, according to a French diplomatic source.
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