ACI Worldwide Inc., which makes software for managing electronic payments, on Thursday boosted the cash part of its offer for S1 Corp. by 50 cents per share and urged S1's shareholders to vote against a proposed deal to combine itself with an Israeli company.

Earlier this month, S1, a financial services software provider, rejected ACI's previous offer of about $540 million in cash and stock for the company, saying that it wasn't in the best interests of its shareholders.

Based on ACI's share price just before the offer was announced, the first offer amounted to $9.50 per share in cash and stock, and the new offer increased it to $10 per share. But ACI's stock has tumbled in the weeks since the first offer was announced, reducing the value of the stock portion of the offer, making it worth $9.29 per share at Wednesday's closing price.

S1 said in a statement that it would review the new offer.

In June, S1 said it was buying Israel's Fundtech for stock valued at about $320 million. Under the terms of that deal, each Fundtech shareholder would get 2.72 shares of S1's stock for each Fundtech share. At the time of that announcement, the offer valued each Fundtech share at $20.51. The companies said the deal was worth about $700 million.

If the Fundtech deal goes through, S1 would own about 55 percent of the combined company and Fundtech shareholders would get a 45 percent stake. The combined company would be based at S1's Atlanta headquarters but would be called Fundtech.

S1 shareholders will vote on the Fundtech deal at a special meeting on Sept. 22. ACI said Thursday that it filed paperwork with the Securities and Exchange Commission in advance of the meeting recommending that S1 shareholders vote against the Fundtech deal and support ACI's bid instead.

If its offer is approved, ACI said the deal could close as early as the fourth quarter. The company said it has secured financing from Wells Fargo Bank NA for the cash part of the deal.

In afternoon trading, ACI shares fell $1.17, or 4.1 percent, to $27.83, while S1 shares rose 2 cents to $8.90.