* Sunrise offers to cut rights issue by up to 1.5 bln Sfr
* Calls No.1 shareholder Freenet "self-serving"
* Freenet has opposed deal, says still open for talks (Adds Freenet statement, Sunrise closing price)
By John Miller and Silke Koltrowitz
ZURICH, Aug 22 (Reuters) - Swiss telecoms firm Sunrise Communications on Thursday stepped up efforts to rescue its takeover of Liberty Global's Swiss unit amid criticism from its top shareholder, saying it had found new synergies and could cut a planned rights issue to fund the deal.
However, Sunrise shares fell more than 6% as analysts picked out some weaknesses in its second-quarter results just as it tries to close the biggest deal of its two-decade history.
German telecoms group Freenet, Sunrise's largest investor, has called the all-cash 6.3 billion Swiss franc ($6.4 billion) takeover of UPC Switzerland unfavourable for Sunrise shareholders and has asked for the price to be cut and risks reallocated.
Criticising Freenet's opposition as "self-serving", Sunrise touted updated expectations of 280 million francs in annual synergies from buying the Liberty business, 45 million more than previously forecast.
Sunrise said the steps it had identified, along with the improved performance of UPC since the deal was announced, would let it increase leverage and reduce the proposed 4.1 billion franc rights issue to pay for the deal by up to 1.5 billion francs.
Sunrise Chief Executive Olaf Swantee said Freenet had rejected that plan.
"Freenet is only interested in a short-term solution to sell as fast as possible at the best possible price to reduce their own debt problem," Swantee told Reuters.
Freenet responded that many investors and analysts shared its view of the deal.
"Despite Sunrise's unacceptable behavior, Freenet and its representatives are still available for constructive dialogue in the interests of Sunrise, existing shareholders and Freenet," it said in a statement.
"However, we will consider all legal and commercial ways and means to fend off damage to Freenet and existing shareholders and to seize opportunities...", Freenet's statement said.
As relationships between the two sides enter a deep chill, Sunrise's board announced it would bar Freenet from deliberations over the UPC deal.
One-off integration costs needed to achieve the higher synergies are expected to increase from 140-150 million to 230-250 million francs, Sunrise said.
Sunrise's second-quarter net income rose to 27 million francs, from 24 million in the year-earlier period. Revenue fell 1.7% to 455 million francs, which Sunrise said resulted from lower mobile hardware and hubbing sales.
Jefferies analysts highlighted a dip in mobile service revenues and pressure from promotions as weaknesses, while praising the Swiss company's cost control that is helping preserve profit margins in a tougher market.
Sunrise shares closed down 6.4% at 72.75 francs, extending their fall this year to about 10%. The shares, while having rebounded from two-year lows this year, are still well down from their 2018 highs, when they flirted with 100 francs.
The UPC deal, which Sunrise aims to close at the end of November, awaits approval from Swiss competition regulators, followed by a shareholder vote on the rights issue.
Freenet's vow to vote its 24.5% stake against the issue could stymie the takeover if other shareholders join the opposition.
Sunrise, whose pursuit of UPC comes amid European industry consolidation being driven by narrowing margins and mounting costs to launch faster 5G services, is hoping UPC will help it to compete better in Switzerland with the country's dominant communication provider, government-controlled Swisscom.
Liberty, set up by U.S. cable pioneer John Malone, is selling off some assets. In December, it said it would sell its DTH satellite TV operations, which serves four eastern European markets, to M7 Group.
($1 = 0.9826 Swiss francs)
($1 = 0.9028 euros)
Reporting by John Miller and Angelika Gruber in Zurich, Editing by Silke Koltrowitz/Mark Potter/Jane Merriman