PARIS (Reuters) - Outdated cross-border tax rules are set to be rewritten after 137 states sought this week to avoid a new trade war over the global multiplication of taxes on digital services.

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Amazon AMZN.O, Facebook FB.O and Google GOOGL.O have strained existing rules to breaking point because such tech giants are able to book profits in low-tax countries like Ireland, no matter where their customers are located.

Government officials agreed at a meeting in Paris to negotiate new rules for where tax should be paid and what share of profit should be taxed when big digital and other consumer-facing businesses do not have a physical presence in the market, the Organisation for Economic Cooperation said.

A growing number of countries are preparing national digital taxes in the absence of a major redrafting of the rules, despite Washington’s threat of retaliatory trade tariffs because it sees such levies as discriminatory against big U.S tech groups.

Tax officials have only a few months to talk ahead of an early July deadline they set for a deal on the complex technical parameters. They aim to reach a full deal by the end of 2020.

“It’s moving fast because what is at stake is a massive trade war,” OECD head of tax policy Pascal Saint-Amans told journalists in Paris.

Paris and Washington agreed a fragile truce last week to set aside a row over France’s digital tax until the end of the year to allow time for the redrafting of international tax rules.

Some of the most intractable negotiations in the coming months are likely to come over a U.S. proposal to let companies choose whether to subject themselves to existing rules or to the future arrangements.

Saint-Amans said the so-called “safe harbour” proposal, which remains to be fleshed out by the Untied States, met with virtually no backing from other countries and would only be dealt with once the other details had been nailed out.

Countries will have to agree to specific profitability thresholds, giving governments rights to tax multinationals and how to take into account the size of a country’s economy.

Some developing countries are concerned the thresholds will suit big developed countries and they also have concerns about a proposal for a binding dispute resolution mechanism.

Governments agreed in Paris that the new rules would apply not only to digital service companies like search engines, social media platforms and cloud computing services but also more traditional companies selling directly to end consumers.

Business-to-business companies and mining and oil firms would not be covered and financial firms would probably be excluded as regulators usually require them to hold capital in the country where their clients are, Saint-Amans said.