* ESMA wants more supervision of foreign platforms
* ESMA studying periodic auctions, may act
* ESMA to say more on consolidated tape
* (Adds more detail)
By Huw Jones
LONDON, June 21 (Reuters) - European Union rules are needed after Brexit to regulate and supervise foreign stock and bond trading venues that want to serve EU investors, the bloc's markets watchdog said on Thursday.
Steven Maijoor, chair of the European Securities and Markets Authority (ESMA) said there was a need for a more consistent approach to how foreign trading venues access the EU.
Many of the platforms that currently offer pan-EU trading are based in London, and Britain is due to leave the bloc next March, becoming a "third country".
Brexit has already prompted the EU's executive European Commission to propose tightening up conditions for foreign investment banks who want to serve EU customers.
"We would welcome an initiative by the Commission with respect to third-country trading venues," Maijoor told a meeting of the Federation of European Securities Exchanges in Vienna.
The EU's MiFID II securities law does not harmonise how foreign platforms can put trading screens in the EU, meaning national watchdogs exercise discretion, leading to inconsistencies.
"A harmonised third-country regime would have the benefit of ensuring a level playing field between EU and non-EU trading venues and mitigate potential risks related to orderly markets, investor protection and ultimately stability," Maijoor said.
Such a regime would cover public exchanges and private venues, such as those operated by banks.
It would also include on-going supervision on top of the current approach of checking at the outset if a foreign financial firm's home rules were "equivalent", or as robust as the rules enforced in the bloc.
"There also needs to be adequate information exchange," Maijoor said.
MiFID II was introduced in January after a year's delay due to the complexity in how it increases transparency in markets to protect investors better.
"Overall, the implementation of MiFID II went quite smoothly," Maijoor said.
The number of share trades in "dark pools" where investors trade anonymously has significantly decreased due to volume caps aimed at encouraging more trading on "lit" public exchanges.
ESMA is studying the sharp increase in periodic auction trading systems -- which match buy and sell orders at certain times during the day rather than continuously -- to see if they are a ruse to get round dark pool caps, Maijoor said.
"If deemed necessary, this may result in further ESMA measures or recommendations."
The EU has long sought a consolidated tape or ticker that combines all prices across Europe's fragmented trading sector.
But it has made little progress due to disagreements between fund managers, banks, data providers and exchanges, raising the prospect of a "mandated" tape through public intervention.
"MiFID II provides for a dedicated review clause, including the possibility that a single consolidated tape may be appointed by ESMA. So you can expect to hear more from us on this issue in the not too distant future," Maijoor said.
Reporting by Huw Jones, editing by Carolyn Cohn and Catherine Evans