* 4 percent limit proposed for new "rent pressure zones"
* Cap may have to be lowered to gain parliamentary support
* Costs damaging Dublin as it chases Brexit business (Adds quotes from opposition party whose support needed)
By Padraic Halpin
DUBLIN, Dec 13 (Reuters) - Ireland's government proposed temporary controls on residential rents on Tuesday to limit annual increases in the two largest cities to 4 percent, but may have to lower the cap and apply it more widely to win support in parliament.
While Ireland was left with a surplus of houses after a 2008 property crash, supply has since failed to come anywhere close to matching demand in the fast-recovering economy, sending rents back above their peak in the "Celtic Tiger" years.
Average rents rose by 11.7 percent year-on-year in the third quarter, a survey showed last month, marking the fastest rate of annual inflation in over a decade with rents in some areas of Dublin now 10 percent above their 2007 peak.
"We're putting a bridle on the horse that has almost been out of control for the last two years," Housing Minister Simon Coveney told a news conference. "This is a really tricky area to get the balance right."
Under the plan, Dublin and Cork city fall under the category of "rent pressure zones", or areas where annual rents have risen by 7 percent or more in four of the last six quarters. They will be the first areas where the three-year caps kick in.
To encourage supply, which Coveney said was beginning to gain momentum, new housing units and renovated vacant units are excluded with rents instead determined by the market rate.
However the minority government does not have enough seats in parliament to enact legislation on its own and requires the cooperation of the main opposition party, Fianna Fail, which will meet later on Tuesday to finalise its position.
"The 4 percent is extremely high... It's off the table. The other issue is that it is not acceptable that this is restricted to Dublin and Cork," Thomas Byrne, a member of the Fianna Fail frontbench, told Newstalk radio.
The lack of supply and resulting price rises have been identified by the government as a risk to its attractiveness to foreign investment, particularly as it tries to win business from firms considering leaving Britain as a result of Brexit.
The proposals will impact Real Estate Investment Trusts (REITS) with exposure in the main residential markets. Shares in Irish Residential Properties (I-RES), Ireland's largest private landlord, closed 2.5 percent lower at 1.16 euros.
"This strategy will provide headwinds for the development of the much needed 'build-to-rent' sector in Ireland and is unlikely to encourage fresh investors into the market," Goodbody analyst Colm Lauder wrote in a note. (Editing by Tom Heneghan and Adrian Croft)