ATHENS (Reuters) - Greece will try to bring more to the table in negotiations for a debt deal and Prime Minister Alexis Tsipras will probably speak with European Commission chief Jean-Claude Juncker by phone on Saturday to try to end the deadlock, a Greek minister said.

Time is fast running out for Greece to secure a cash-for-reforms deal with its international creditors to avoid a default at the end of June that could turf it out of the euro zone. With nervy depositors pulling billions out of Greek banks, Athens may have to impose capital controls within days to staunch the flow.

It was not immediately clear how far Greece's leftist government, which won a January election vowing to pull its people out of austerity, is willing to bend in order to secure an agreement or what kind of additional offers it could make.

While Greece has dug its heels over demands for pension cuts and some tax rises, its leaders have continued to sound upbeat ahead of an emergency euro zone summit on Monday.

"We will try to supplement our proposal so that we get closer to a solution," State Minister Alekos Flabouraris told Greek Mega television in a morning news show.

"We are not going there with the old proposal. Some work is being done to see where we can converge, so that we achieve a mutually beneficial solution."

The European Central Bank has kept Greek lenders afloat and on Friday raised the ceiling on so-called emergency liquidity assistance, which the banks rely on to keep their doors open, by 1.8 billion euros.

A close aide to Tsipras, Flabouraris said he was confident the ECB would not cut off funding as this would set off a domino effect and topple lenders in other vulnerable parts of Europe.

EU chief Juncker has been seen as more sympathetic to Greece's position, although he has reportedly warned Athens not to rely on him to avert a collapse in the debt talks.

"I am among those who believe that we are heading towards a solution," Flabouraris said. Asked whether there would be a teleconference on Saturday, he said: "I believe that there will be one. It has not been arranged yet. Tsipras is flying back from Moscow. He will be in Athens after 12.30pm (0530 ET). I believe that some kind of communication will be sought (by Juncker) in the evening hours."

(Writing by Matthias Williams; Editing by Toby Chopra)