JERUSALEM, June 28 (Reuters) - Prime Minister Benjamin Netanyahu's ruling coalition postponed a preliminary parliamentary reading on Wednesday of a bill the central bank chief had said would threaten the Bank of Israel's independence.

Yinon Azulay, the parliament member who proposed the bill which would force banks to pay interest on checking accounts and give final approval on setting the rate to the finance minister, said the vote would take place next week instead.

Azulay said that after consultations with Netanyahu, he had decided to put the vote off in order to give the banks time to respond to a request made to them by Bank of Israel Governor Amir Yaron to improve consumer interest rates.

Yaron, saying the bill crossed a "red line" and would harm the bank's independence and ability to conduct monetary policy, had asked banks pass on higher interest rates to customers' accounts as they have to mortgages and other loans.

On Wednesday, Yaron and Israel's banking supervisor met Finance Minister Bezalel Smotrich and senior treasury officials to discuss regulation and promoting competition in the banking system, a joint statement said. Among Finance Ministry proposals discussed was for a tax on excess bank profits, it added.

Mizrahi-Tefahot, Israel's third-largest bank, on Wednesday said it would pay 2% interest on checking accounts while lowering interest rates on balances below zero.

This followed a similar move by market leader Leumi earlier this month. Yaron has said each bank should decide on its own course of action.

Azulay's bill, aimed at benefiting the public amid a sharp jump in interest rates on loans, won the government's backing on Sunday and was due for a preliminary reading in parliament on Wednesday before review, possible changes and three more votes.

But on Tuesday, Yaron in a letter to Netanyahu, warned that the proposed legislation, particularly in giving the finance minister final say on interest rate levels, was a "serious blow" to the central bank's independence.

The shekel was down another 0.4% after weakening by some 1% versus the dollar on Tuesday after Yaron's warning. Tel Aviv share indices were marginally higher.

The proposed legislation was the latest move by members of Netanyahu's coalition critical of recent rate hikes, despite Netanyahu's repeated calls for maintaining central bank independence.

The Bank of Israel has also been at odds with the government on its plans to overhaul the judiciary, which the bank says could compromise institutional independence.

David Bitan, chairman of parliament's Economics Committee, criticised the delay to the banking bill vote, saying it was a result of "intervention" from Yaron and the banks, and the details could have been worked out before the final vote. (Editing by Peter Graff, Toby Chopra and Alistair Bell)