* Swiss draw up plans to ban trading Swiss shares on EU exchanges
* Won't implement if EU extends approval of Swiss bourse rules
* Measures come against backdrop of Swiss-EU treaty negotiations (Adds comment from finance ministry, European Commission)
ZURICH, June 8 (Reuters) - The Swiss government threatened on Friday to ban trading of Swiss shares on exchanges in the European Union in a tit-for-tat battle with Brussels over stock market rules that could put a severe dent in cross-border trading.
The row casts a shadow over ties between neutral Switzerland and its main trading partner that had been improving after the Swiss parliament in 2016 skirted voters' demand in a referendum for immigration quotas for EU citizens.
Bern said the contingency measures to protect domestic stock exchanges could be issued in December should the European Commission not extend beyond year's end its recognition of Swiss market rules, which lets EU investors trade on Swiss bourses.
The Commission in December linked any extension to progress on a new bilateral treaty it wants with non-member Switzerland, upping the pressure on Bern to strike a deal.
At the time, the Swiss government promised retaliatory steps that did not materialize as ties thawed again. The measures unveiled on Friday could complicate the treaty talks, although the finance ministry stressed they were unrelated.
"Plan A is clearly still to make progress in negotiations with the EU so that we can get unlimited recognition of bourse equivalency or at least a one-year extension, and we are confident we can achieve this," Swiss Finance Minister Ueli Maurer told a news conference in Bern.
If not, the Swiss government will issue an ordinance requiring foreign trading venues to get Swiss recognition for trading Swiss shares. EU trading venues would not qualify, but other venues like New York, Singapore or Hong Kong would.
Swiss officials hope this would encourage more trading of Swiss stocks in Switzerland.
Maurer said Switzerland had to ready defensive steps.
"If we didn't get equivalence (from the EU) and didn't adopt protective measures, the bourse expects trading volume would collapse by 70 to 80 percent. Of course this would not be manageable," he said.
The Swiss exchange is fourth-largest on the continent with listed companies worth 1.3 trillion Swiss francs ($1.32 trillion).
In Brussels, the Commission took note of the Swiss announcement. "The European Commission's priority is to move forward on our discussions on the overall negotiations on an institutional framework agreement with Switzerland," a spokesperson added.
SIX Swiss Exchange said it was still analyzing the steps.
By allowing Swiss exchanges only one year of access to the single market, Brussels increased the pressure on Switzerland to agree on a formal treaty, which the Swiss far right opposes. A patchwork of 120 bilateral accords now governs ties.
Both sides aim to strike a deal in principle this year. But diplomats say differences remain over handling state aid and measures to protect the Swiss labor market, while there has been progress on using arbitration panels to settle disputes.
($1 = 0.9858 Swiss francs) (Additional reporting by Robert-Jan Bartunek in Brussels; Editing by Toby Chopra)