The two-month grace period covers all types of visas, including tourist and expired residency permits
Facebook, Google, Amazon, and other large tech companies have come under criticism for cutting their tax bills by booking profits in low-tax countries regardless of the location of the end customer, practices seen by many as unfair.
The new rules mean higher tax burdens for large multi-national firms, but will also make it more difficult for countries like Ireland to attract foreign direct investment with the promise of ultra-low corporate tax rates.
"It sounds like we have a strong consensus," U.S. Treasury Secretary Steven Mnuchin said on Saturday at a two-day meeting of G20 finance ministers in the southern Japan city of Fukuoka.
"So now we need to just take the consensus across here and deal with technicalities of how we turn this into an agreement."
Mnuchin spoke at a panel on global taxation at G20 after the French and British finance ministers expressed sympathy with Mnuchin's concerns that new tax rules do not discriminate against particular firms.
Big internet companies say they follow tax rules but have paid little tax in Europe, typically by channelling sales via countries such as Ireland and Luxembourg, which have light-touch tax regimes.
The G20's debate on changes to the tax code focus on two pillars that could be a double whammy for some companies.
The first pillar is dividing up the rights to tax a company where its goods or services are sold even if it does not have a physical presence in that country.
If companies are still able to find a way to book profits in low tax or offshore havens, countries could then apply a global minimum tax rate to be agreed under the second pillar.
"We cannot explain to a population that they should pay their taxes when certain companies do not because they shift their profits to low-tax jurisdictions," French Finance Minister Bruno Le Maire said at the panel.
Britain and France have been the most vocal about the need for a so-called "digital tax," arguing that corporate tax codes are no longer fair in the age of the large-scale provision of services and the sale of consumer data over the Internet.
The U.S. government has expressed concern in the past that the European push for a "digital tax" unfairly targets U.S. tech giants.
However, Mnuchin said on Saturday G20 countries should issue "marching orders" to their respective finance ministries to negotiate the technical aspects of an agreement after listening to presentations by Le Maire and British finance minister Philip Hammond.
Officials from major countries are expected to meet again twice this year to hammer out the finer details with the aim of finalising an agreement next year.
Earlier this year, countries and territories agreed a roadmap aimed at overhauling international tax rules, which have been overtaken by development of digital commerce.
The two-month grace period covers all types of visas, including tourist and expired residency permits
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