* Capital increase could pave way for bid by Slim
* Core shareholders will subscribe increase
* Aim is to pay down debt, strengthen balance sheet (Adds details on capital increase, background)
By Adrian Croft and Julien Toyer
MADRID, Dec 17 (Reuters) - The board of Spain's FCC approved a 709.5 million euro ($766.6 million) capital increase on Thursday, the company said, in a move that may pave the way for Mexican billionaire Carlos Slim to take control of the firm.
The proceeds will be used to pay down debt and to strengthen the balance sheet of the debt-laden construction and services company, which has struggled to reshape its business as Spain emerges from a punishing economic downturn that caused a construction slump and hit infrastructure spending.
FCC's shares have fallen more than 50 percent this year.
FCC said it would issue 118.3 million new shares priced at 6 euros per share, above Thursday's closing price of 5.564 euros.
The core shareholders, Esther Koplowitz and Mexican billionaire Carlos Slim's holding company Inversora Carso group , have pledged to fully subscribe their share of the capital increase and Inversora Carso has committed to buy any unsubscribed shares, FCC said in a statement.
Slim became FCC's largest shareholder with a 25.6 percent stake last year after buying more than 50 percent of a previous $1.3 billion rights issue in a deal with Koplowitz, daughter of the company's founder, who has a 22.5 percent stake.
The new rights issue could push Slim's company above the 30 percent threshold that would require him to launch a full bid for FCC under Spanish takeover rules.
The six euro a share price of the capital increase, higher than the 5.564 euros closing price on Thursday, could be an indication of the price at which Slim could pitch a takeover offer, a source familiar with the company's situation said.
FCC said it would use proceeds from the capital increase to buy back its so-called "Tranche B" debt at a discount and to financially support its Cementos Portland unit.
In a bid to put the group on a firmer footing, Slim's Mexican colleague Carlos Jarque was appointed as the new chief executive in August. Talks were also opened with creditors to refinance the "Tranche B" debt that the company has said it wants to cancel to give it a more efficient capital structure.
FCC said it intended to subscribe to a capital increase at property firm Realia, indicating that part of the proceeds of the capital increase would be used for this purpose.
Realia is controlled by Slim through FCC's 37 percent stake and a 25 percent stake bought in March by his own property group Inmobiliaria Carso.
FCC posted a net loss of 13.6 million euros in the nine months to September, hit by a weak performance in its domestic market that offset growth in its foreign business. Core profit (EBITDA) rose 2 percent on the period to 593.4 million euros. (Reporting by Adrian Croft and Julien Toyer; Editing by Tom Heneghan)