LONDON (Reuters) - Security firm G4S will donate 2.5 million pounds ($3.9 million) to British military sports and welfare organizations to thank troops who stepped in to secure Olympic venues after it failed to provide enough guards, the government said on Monday.

Media coverage ahead of the London 2012 Games was dominated by G4S's admission it could not supply all of a promised 10,400 guards for the two-week sporting festival, which closed on Sunday.

An additional 4,700 military personnel were mobilized to join 13,500 troops already earmarked for venue security after G4S's last-minute admission it had problems recruiting sufficient staff.

Shares in G4S, the world's largest security firm, fell 17 percent in the days following the disclosure, but have since recovered around half their losses to close at 262 pence on Friday.

"This contribution from G4S is welcome news for the service welfare funds and will go some way to recognizing the inconvenience and extra burden that this commitment has placed upon our forces and their families," said Defence Secretary Philip Hammond.

G4S Chief Executive Nick Buckles admitted its management of Olympic security staffing had left the company's reputation in tatters, in a chastening hearing last month before British legislators in parliament.

G4S has said it could lose up to 50 million pounds on the Olympics security contract, worth 284 million pounds. Buckles told parliament the group still expected to take its 57 million pound management fee from the Games.

But the firm's second-largest shareholder, money manager Invesco, has backed Buckles, saying one contract failure should not lead to the G4S chief executive being axed.

(Reporting by Tim Castle; Editing by Alison Birrane and Jane Baird)