* Iran rejects proposal for immediate ceasefire

* Taiwanese and South Korean stocks climb

* Indonesian rupiah hits record low

By Niket Nishant

April 7 (Reuters) - Emerging market stocks climbed on

Tuesday, cruising towards their third consecutive session of

gains as investors weary of the relentless headlines from the

Middle East picked winners selectively.

Repeated false dawns and harsh rhetoric from both sides have

dimmed investors' hopes of a swift end to the U.S.-Israel war

with Iran, now in its sixth week.

Iran rejected a U.S. proposal for an immediate ceasefire and

the lifting of its effective blockade of the Strait of Hormuz,

according to a source aware of the ​plan. U.S. President Donald

Trump has imposed a deadline of 8 p.m. Tuesday (0000 GMT) for a

deal to be reached.

With few assets looking attractive, traders looked harder

for pockets of strength.

A 2.8% gain in TSMC drove Taiwan's AI-heavy

benchmark 2% higher, while South Korea's Kospi index

rose 0.8%.

The MSCI index of emerging market equities gained

1%.

INFLATION AND POLITICS IN FOCUS

Czech stocks rose 1.2% as data showed that surging

fuel prices drove a less-than-expected jump in March inflation.

Later this week, inflation figures are also due for Hungary,

which is gearing up for an election that is expected to be a

tough challenge for nationalist Prime Minister ​Viktor Orban.

Hungarian equities climbed 1.8% while the forint

rose 0.3% against the dollar.

"We expect a tight race," said ING's EMEA FX strategist

Frantisek Taborsky, referring to the election.

"Hungarian assets are the only ones in CEE (Central and

Eastern Europe) to have visibly reacted to the local story and

have somehow deflected the global influence. We've seen the

forint outperforming the rest of the region in recent days,

which is likely to continue this week as well."

In Poland, the equities benchmark rose 1% and the

zloty was flat against the euro, following three

straight days of gains.

Elsewhere, South African stocks were largely

steady, while the rand was up 0.3% against the dollar.

The African Export-Import Bank approved a $10 billion

programme to help African and Caribbean economies, as well as

their banks and companies, counter the severe economic shocks

triggered by the Middle East conflict.

INDONESIAN RUPIAH TUMBLES

In Asia, the Indonesian rupiah breached the 17,100

level against the dollar for the first time, defying the central

bank's efforts to prop it up, as energy shocks and lingering

fiscal and governance concerns chased foreign investors away.

"Policymakers will have no choice but to hike fuel prices by

up to 5% in the months ahead. Crucially, Indonesia's fiscal

position was already shaky before the Iran war started,"

economists at Pantheon Macroeconomics wrote.

Equities also slipped 0.3%, while in neighbouring

Thailand, stocks rose 0.7% after a surprise drop in

March's consumer prices.

The ministry, however, warned of a potentially significant

increase in inflation in the second quarter.

"We maintain that the (central bank) will remain on hold

until the end of our forecast horizon to 2027," Pantheon wrote.