Hearts say they remain in a "perilous position" because of a near £800,000 shortfall in funding for the season - despite £1.05m raised by a share issue.
But they believe that big attendances at future matches "would make up almost the entire shortfall".
"Much of the rest could be generated through ticket sales for the Scottish Communities League Cup semi-final against Inverness," they state.
Four thousand supporters signed up to the scheme, according to the club.
The club's majority shareholder Vladimir Romanov had put approximately 10% of his stake in the company up for sale.
And the majority of cash raised has come from supporters who have taken part in fundraising activities during the past eight weeks.
Supporters have been urged to continue to attend matches in high numbers in a bid to reduce the shortfall after £161,000 was raised in "unbudgeted" ticket sales from the matches at home to St Mirren, Celtic and Aberdeen.
Hearts director Sergejus Fedotovas said fans had "given the club a lifeline in its darkest hours" despite not matching Hearts' initial target of £1.79m.
Fedotovas, right-hand man to majority shareholder Vladimir Romanov, said on the club's official website: "The best way that we can all push through this difficult situation is by supporting the team and buying half season tickets and match tickets.
"Together we can emerge a leaner, stronger football club and I expect that the supporters will be the ultimate beneficiaries as we progress towards making Hearts a club that is one of the most progressive and supporter-centric in the country."
When the share issue scheme was launched, the prospect of supporter ownership was mooted and discussions with Supporters Direct Scotland are continuing, according to Fedotovas.
"We are now working on the most suitable model that will give the club the best long-term chance of development under true supporter control," he said.
"We expect to announce further details of this in the early part of 2013."
The share offer closed at on Wednesday, and the amount raise may rise as final applications are processed in the next few days.
Due to supporter requests, the club will also accept completed applications and payment until Sunday's game against Dundee United.
The news came on the day that Hearts had their signing embargo extended indefinitely by the Scottish Premier League for not paying "a number of bonuses and appearance payments due to players".